Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Physical quantities and
units of measurement.
Marco Caniato
Free University of Bozen
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
A physical phenomenon or system can be described through a number of attributes,
useful to characterize its nature, state or behavior
A physical quantity Q
characterizing the system
a magnitude or value: |Q|
level, intensity
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
The values of a given quantity in different systems can be compared to assess
whether they are or not equivalent
Comparison of values
Kinds or Classes
Certain class
Certain magnitude
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Measurement is the assignment of a number or symbol to a quantity in order to
describe or express its value. To compare quantities of the same class, we can rely on
measurement.
Comparison of measurements
measure
same class
association with a number
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Example: Quantity, magnitude and class
length
length
length
width
width
width
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Measurement can be direct, when it implies only a comparison between entities of
the same class, or indirect, when it is based on relations between the entities to be
measured and other measurable quantities.
system of empirical relations
among elements of the class
among elements of the class Q
formal correspondence
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Classifications: Ordinal scale.
In ordinal scales the set of relations is given by an empirical order system:
R = [Q, ~, <, >]
relations are complementary
if Q1<Q2 then Q2>Q1
any couple of quantities
only one of the three is true
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Example: Mohs’ scale of hardness: it permits to measure the hardness of a surface
Talc
Apatite
Diamond
absolute
hardness 1
absolute
hardness 5
absolute
hardness 10
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Measurement can be indirect, when it is based on relations between the entities to be
measured and other measurable quantities. They can be measured through either (i)
associative or (ii) derived measurement.
Associative measurements
any quantity non measurable Q
Q is ordered within the class Q
associated with other measurable
quantity X
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Example: Celsius and Fahrenheit
Celsius and Fahrenheit scales are based on the relation with the length of the
thermometric liquid in the capillary tube. Also the definition of the scale corresponds to
a linear scale: two measures are selected for reference temperatures, providing their
distance. One of the reference temperatures in the case of Celsius scale is also the
arbitrary zero of the scale.
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Measurement can be derived, when the value of quantity to be measured can be
expressed in mathematical terms as a function of the values of a set of other
measurable quantities, called fundamental or primary quantities.
a quantity Q
Q = F(X,Y,Z). Q is derived
associated to set of quantities X, Y, Z
numerical law exists between
quantities
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Example: Density
Introducing density as a property of a given material, assuming the same value for all
objects of the same material. It can be related to the ratio ρ between the mass m of
the object and its volume V, such that ρ=m/V is constant for all the objects of the same
material. Whenever objects are arranged in order of density, intended as a quantity,
they will be ordered according ρ, intended as a measure of density.
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Example: Velocity
Velocity can be introduced as a derived quantity, defined as the ratio between the
distance travelled and the time duration.
=
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
The concept of dimensions can be introduced. In general, but in particular for
fundamental quantities, quantities of the same kind of Q have the same dimensions,
as a consequence of the fact that those quantities can be compared and measured on
the same scale
derived quantity
Q = Xx Yy Zz (all dimensions)
derived measure
derived dimension(s)
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Example: Force
Force can be said to have the dimensions of a mass times the dimensions of an
acceleration.
=
·
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
When taking a direct measurement, the quantity to be measured is generally
compared with a reference one and its multiples or submultiples.
length
width
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
In both analog instruments and digital instruments, the measurement is affected by
approximations leading to uncertain measures. Overall uncertainty expresses the
estimated distance between the actual value, which is by definition not known, and the
measured one.
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
In such cases uncertainty arises because of the resolution or sensitivity of the
instrument. The quality of construction of the instrument can also bring some
uncertainty, considering for instance possible approximations in the reproduction of
the reference units or in the alignment to the zero of the scale, or the stability of the
instrument.
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Two attributes can describe the quality of a measure in terms of uncertainty: accuracy
and precision. Accuracy refers to the quality of a measure to be close to the real
value. The more accurate, the closer a measure is to the real value. Inaccuracy can
be reduced comparing and tuning the instrument with respect to a reference one, in a
process named calibration.
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Precision refers to the repeatability of a measurement. The more precise, the less
disperse a repeated series of measures is. For a set of measurements, normally
distributed, standard deviation can provide a measure of the precision.
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Accuracy and precision can be determined using many methodologies.
σ
=
1
=1
−
graphically
2
∆
=
1
=1
|
regression
−
|
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Example: comparison of measurement methodologies
Methodology
System 1
System 2
Parameter 2
Parameter 1
dev. st.
r2
dev. st.
Parameter 2
Parameter 1
r2
dev. st.
r2
dev. st.
r2
A
5.9
4.8
0.931
--
--
--
9.2
7.7
0.931
--
--
--
B
2.8
2.0
0.951
3.0
2.6
0.891
5.4
4.2
0.973
8.22
6.6
0.788
C
--
--
--
--
--
--
2.6
2.3
0.987
8.22
6.6
0.788
D
3.4
3.0
0.959
3.3
3.3
0.902
2.7
2.3
0.990
8.12
6.9
0.826
E
2.4
1.92
0.965
3.0
2.6
0.920
2.3
1.9
0.992
8.15
6.6
0.879
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Example: comparison of measurement methodologies
Q-Q plot. Measurements vs. Std. model. Bare
structure
Q-Q plot. Measurements vs. TMM. Bare
structure
Q-Q plot. Measurements vs. simplified FEM. Bare
structure
60
60
60
55
55
55
50
50
50
45
45
45
40
40
40
35
35
35
30
30
30
25
25
25
20
20
20
15
15
15
10
10
10
15
20
25
30
35
40
45
50
55
60
10
10
15
20
25
30
35
40
45
50
55
10
60
Q-Q plot. Measurements vs. TMM + Simplified
FEM. Bare structure
60
55
50
45
40
35
30
25
20
15
10
10
15
20
25
30
35
40
45
50
55
60
15
20
25
30
35
40
45
50
55
60
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
When reporting a measure, there are different notations to indicate the uncertainty. It
can make some difference when considering analog or digital measurements.
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Consider the choice is for 158.3, then the reading will be:
15.83 cm or 158.3 mm.
Where 3 is the estimated and so uncertain digit. Although this intends to be a good
estimation of the actual measure, we can report that uncertainty is on the last digit. It
also means that the reported measure is actually affected by an estimated uncertainty
of ± half the resolution of the instrument:
158.3 ± 0.5 mm
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Imagine the weigh of an object is 24.4 g and it has to be measured on a digital
balance with a maximum resolution of 1 g. When the object is put onto the balance,
the reading of the display will provide 24 g. It can be supposed at a first approximation
that the reported measure is the result from rounding of the actual value, so it will not
be possible to argue whether the weigh to be measured is 23.4 or 24.4 g. Therefore,
the uncertainty is 0.5 mm.
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
It is worth noting that in both cases measures are expressed with a given number of
figures or digits. Not all figures have the same importance and meaning.
145,98000
0.0001583 km, 0.1583 m, 15.83 cm, 158.3 mm
0.024 kg, 24 g
0.024 kg, 24 g
24 g ≠ 24.0 g ≠ 24.00 g
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
For indirect measurement of derived quantities the effect of the uncertainty of each
fundamental quantity has to be assessed, taking into account the defining expression.
The same happens when performing operations with measures.
addition (x ± Δx)+ (y ± Δy) = x+y ±( Δx+ Δy)
subtraction (x ± Δx)– (y ± Δy) = x–y ± ( Δx+ Δy)
product (x ± Δx) ×∙(y ± Δy) = x × y ± (x Δy + y Δx)
division (x ± Δx)/(y ± Δy) = x/y ± (x Δy + y Δx)/(y2)
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Geographical or cultural contexts have consolidated over time the local definition and
use of a variety of sets of units of measurement, different not only for the choice of
units, but also for the choice of the base and derived quantities, most of the times
without paying much attention to their coherence.
The process that led to the definition of the International System (SI) started from the
metric decimal system. That was introduced in France at the time of the French
Revolution, even if after an initiative by the king Louis XVI, with the construction of the
platinum samples of meter and kilogram, respectively as a unit of length and mass.
1832
1860
1874
1939
1946
1971
1875
1889
1901
59 Member States and 42 Associate States
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
The International System of Units, has been defined through the choice of a suitable
set of base units and of coherent derived units, starting from the corresponding
products of powers. The first step in the definition of a system of units, namely the
choice of base quantities is implicit in the SI. The definition of an International System
of Quantities (ISQ), corresponding to the SI units, is the aim of the international
standard ISO/IEC 80000
In the past, different types of definitions for the base units have been used, such as:
(i) artefacts;
(ii) specific physical states;
(iii) idealized experimental prescriptions,;
(iv) constants of nature.
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
The 26th meeting of the CGPM (2018) approved the revision of the SI, changing the
definition of the kilogram, the ampere, the kelvin and the mole, in order to have all
units defined from universal constants
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Seven base units and their associated quantities are then defined from the seven
constants. Each quantity has a typical symbol, unit of measurement, unit symbol and
dimension.
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical
valueof the caesium frequency ∆νCs, the unperturbed ground-state hyperfine transition
frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit
Hz:
1 s = 9 192 631 770 / ∆νCs
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
The metre, symbol m, is the SI unit of length. It is defined by taking the fixed
numerical value of the speed of light in vacuum c to be 299 792 458 when expressed
in the unit m s−1, where the second is defined in terms of the caesium frequency ∆νCs
1 m = c / 299 792 458 × s = c / 299 792 458 × 9 192 631 770 / ∆νCs
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed
numerical value of the Planck constant h to be 6.626 070 15 × 10−34 when expressed
in the unit J s, which is equal to kg m2 s−1,where the metre and the second are defined
in terms of c and ∆νCs
1
=
%
. " #$# %& · %#'() *+
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
1
=
1
ℎ
6.626 070 15 · 10123
=
9 192 631 770
9
299 792 458
"
678
9 192 631 770
678
299 792 458"
ℎ 678
6.626 070 15 · 10123 · 9 192 631 770
9"
"
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Once the base quantities have been chosen, all other quantities, with the exception of
counts, are derived quantities, which may be written in terms of base quantities
according to the equations of physics.
dim Q = Tα Lβ Mγ Iδ Θε Nζ Jη
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Twenty-two of the derived units in the SI have special names
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
All other SI units are combinations of some of these. Some of those whose names
and symbols are based on derived units with special names and symbols are reported
below
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Prefixes can be used with unit symbols to indicate decimal multiples and submultiples
of units of measurement in the range from 10-24 to 1024. In particular only power
multiples of 3 are considered, except for the range between 10-3 and 103 for which all
multiples are available
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Symbols for both prefixes for powers of ten lower than or equal to 3, then up to kilo
(k) and units of measurement with names not deriving from the names of scientists
(mol, s, rad, km, etc.) are never capitalized. All other prefixes from mega (M) on or
units named after a scientist are always capitalized (N, J, W, A, V, etc.)
23 °C, but not 23°C;
5,6 m, but not 5,6m
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
The internationally recognized symbol % (percent) may be used with the SI. When it is
used, a space separates the number and the symbol %.
As concerns the algebra of symbols, the following rules hold:
1. Products:
N×m, N·m, N m, but never Nm
2. Divisions:
m/s2,
*
,
8+
m·s-2, m s-2, but never m/s/s
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
1. symbols of prefixes are written before symbols of units, without any blank space or
other characters
2. the group made of prefix and symbol is a unique entity, to which power,
multiplication or division can be applied to get derived quantities:
1 cm3 = (10-2 m)3 = 10-6 m3, but not 10-2 m3
1 ms-1 = (10-3 s)-1 = 1/(0,001 s), not 10-3 s-1 or 0,001/(1 s))
3. never use double prefixes
4. never use prefixes alone:
106/m3, but not 1 M/m3
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
The imperial system is based on different units of measurement for length, mass,
temperature, so that also derived units are affected by the base ones.
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Energy and Energy transfer.
Marco Caniato
Free University of Bozen
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Energy
Whether we realize it or not, energy is an important part of most aspects of daily life
Energy exists in numerous forms such as thermal, mechanical, electric, chemical, and
nuclear
E=mc2
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Energy
We are familiar with the conservation of energy principle, which is an expression of
the first law of thermodynamics
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Forms of Energy
Thermodynamics provides no information about the absolute value of the total energy.
It deals only with the change of the total energy, which is what matters in engineering
problems
In thermodynamic analysis, it is often helpful to consider the various forms of energy
that make up the total energy of a system in two groups: macroscopic and
microscopic
U
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Forms of Energy
The macroscopic energy of a system is related to motion and the influence of some
external effects such as gravity, magnetism, electricity, and surface tension
The energy that a system possesses as a result of its motion relative to some
reference frame is called kinetic energy
=
+
=+
=
[J] [J]
where v is the velocity and m the mass of the moving body
where g is gravitation acceleration and z the elevation of the center of gravity
[J]
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Forms of Energy
Most closed systems remain stationary during a process and thus experience no
change in their kinetic and potential energies. ∆
Stationary systems!!!!
0
=
+
0
[J]
+
=
[J]
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Internal Energy
Internal energy is defined earlier as the sum of all the microscopic forms of energy of
a system. It is related to the molecular structure and the degree of molecular activity
and can be viewed as the sum of the kinetic and potential energies of the molecules∆
Molecular translation
Molecular kinetic rotation
Molecular kinetic vibration
Electron kinetic rotation
Electron and nuclear spin
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Internal Energy
The portion of the internal energy of a system associated with the kinetic energies of
the molecules is called the sensible energy∆
U
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Internal Energy
The internal energy is also associated with various binding forces between the
molecules of a substance∆
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Internal Energy
This is a phase-change process. Because of this added energy, a system in the gas
phase is at a higher internal energy level than it is in the solid or the liquid phase. The
internal energy associated with the phase of a system is called the latent energy.
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Internal Energy
An atom consists of neutrons and positively charged protons bound together by very
strong nuclear forces in the nucleus and negatively charged electrons orbiting around
it. The internal energy associated with the atomic bonds in a molecule is called
chemical energy
C3H8 + O2
3 CO2 + 4 H2O
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Internal Energy
The nuclear forces are much larger than the forces that bind the electrons to the
nucleus. The tremendous amount of energy associated with the strong bonds within
the nucleus of the atom itself is called nuclear energy
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Internal Energy
The forms of energy already discussed, which constitute the total energy of a system,
can be contained or stored in a system, and thus can be viewed as the static forms of
energy.
static
dynamic
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Internal Energy
The only two forms of energy interactions associated with a closed system are heat
transfer and work.
Temperature driven
Other cases
Heat transfer
Work
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Mechanical Energy
Distinction should be made between the microscopic and macroscopic kinetic energy
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Mechanical Energy
The mechanical energy can be defined as the form of energy that can be converted to
mechanical work completely and directly by an ideal mechanical device
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Mechanical Energy: example and exercitation
A pump transfers mechanical energy to a fluid by raising its pressure and a turbine
extracts mechanical energy from a fluid by dropping its pressure
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Mechanical Energy: example and exercitation
The
ℎ
! of a flowing fluid can be expressed as:
.
=
.
" $
+
+
#
2
[W]
Flow energy
.
∆ =
.
& '&(
)
+
' (
+
−
+
[W]
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Mechanical Energy: example and exercitation
Application to wind turbine:
A site evaluated for a wind farm is observed to have steady winds
at a speed of 6 m/s. Determine the wind energy per unit mass (i) for
a mass of 10 kg and (ii) for a flow rate of 1154 kg/s for air
$
2
=
.
=
.
$
2
= 10 .
= 1154 .
6
6
2
/1
2
= 180 3
/1
= 20.8 .7
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Energy transfer by heat
Energy can cross the boundary of a closed system in two distinct forms: heat and
work
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Energy transfer by heat
Heat is defined as the form of energy that is transferred between two systems (or a
system and its surroundings) by virtue of a temperature difference
Room hair 25 °C
no heat transfer
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Energy transfer by heat
Several phrases in common use today
heat addition/rejection
Heat loss
heat absorption
resistance heating
body heat
heat generation
heat source
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Energy transfer by heat
Heat is energy in transition. It is recognized only as it crosses the boundary of a
system
2J
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Energy transfer by heat
A process during which there is no heat transfer is called an adiabatic process
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Energy transfer by heat
The amount of heat transferred during the process between two states (states 1 and
2) is denoted by Q12, or just Q. Heat transfer per unit mass of a system is denoted q
8=
9
[
3
]
.
Sometimes it is desirable to know the rate of heat transfer instead of the total heat
transferred over some time interval
9 = : 9; <=
[3]
9 = 9; =[3]
[3]
(
45 kJ
Q= 45 kJ
m = 3 kg
∆ t = 15 s
9; = 675 kW
q = 15 kJ/kg
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Energy transfer by work
Work, like heat, is an energy interaction between a system and its surroundings
The work done per unit time is called power and is denoted W;
>=
7
[
7 = : 7; <=
(
7 = 7; =[3]
3
]
.
[3]
45 kJ
[3]
W= 45 kJ
m = 3 kg
s= 15 s
7; = 675 kW
w = 15 kJ/kg
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Energy transfer by work
The generally accepted formal sign convention for heat and work interactions is as
follows: heat transfer to a system and work done by a system are positive; heat
transfer from a system and work done on a system are negative.
Qout
Win
-Q
-W
Qin
Wout
+Q
+W
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Energy transfer by work
Heat and work are energy transfer mechanisms between a system and its
surroundings and there are many similarities between them:
1) Boundaries
p
1
2) Systems possess energy, but not heat or work
3) Both are associated with a process, not a state
2
4) Both are path functions
3
7
V
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Energy transfer by work
Path functions have inexact differentials designated by the symbol δ. Therefore, a
differential amount of heat or work is represented by δ Q or δ W, respectively, instead
of dQ or dW
Properties, however, are point functions (i.e., they
depend on the state only, and not on how a system
reaches that state) and they have exact differentials
designated by the symbol d
p
1
2
: <@ = @+ − @ = ∆@
+
: B7 = 7+,
+
Not ∆W!!!
3
7
V
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Training
Baking a cake in a oven. Heat transfer? Work?
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Training
Baking a cake in a oven. Heat transfer? Work?
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Training
Baking a cake in a oven. Heat transfer? Work?
Engineering Thermodynamics and Heat and Mass Transfer
Prof. Marco Caniato
Mechanical work
There are several different ways of doing work, each in some way related to a force
acting through a distance
W = Fs
W = D+ E<1
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Thermodynamics: basic concepts.
Marco Caniato
Free University of Bozen
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Thermodynamics
Thermodynamics can be defined as the science of energy. Although everybody has a
feeling of what energy is, it is difficult to give a precise definition for it. Energy can be
viewed as the ability to cause changes
Conservation of energy: during an interaction, energy can change from one form to
another but the total amount of energy remains constant
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Thermodynamics
All activities in nature involve some interaction between energy and matter; thus, it is
hard to imagine an area that does not relate to thermodynamics in some manner
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
System and control Volumes
A system is defined as a quantity of matter or a region in space chosen for study
surroundings
Boundary
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
System and control Volumes
Systems may be considered to be closed or open, depending on whether a fixed
mass or a fixed volume in space is chosen for study
mass
Closed
system
energy
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
System and control Volumes
Consider the piston-cylinder device
Closed
system
Gas 1 kg, 2 m3
Gas 1 kg, 1 m3
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
System and control Volumes
An open system, or a control volume, as it is often called, is a properly selected region
in space. It usually encloses a device that involves mass flow such as a compressor,
turbine, or nozzle.
Control
volume
Real
boundary
Imaginary
boundary
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
System and control Volumes
A control volume can be fixed in size and shape, as in the case of a nozzle, or it may
involve a moving boundary
Moving
boundary
Fixed
boundary
Control
volume
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
System and control Volumes
Example of open system
Hot water
Control
volume
(water
heater)
Cold water
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Property of a system
Any characteristic of a system is called a property. Some familiar properties are
pressure P, temperature T, volume V, and mass m.
extensive
m
m½ m
½m
V
V½ V
½V
T
T
T
T
P
P
P
P
ρ
ρ
ρ
ρ
intensive
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
State and Equilibrium
Consider a system not undergoing any change. At this point, all the properties can be
measured or calculated throughout the entire system, which gives us a set of
properties that completely describes the condition, or the state, of the system.
m = 2 kg
m = 2 kg
T = 25 °C
V = 1.5
m3
T = 25 °C
V = 3 m3
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
State and Equilibrium
There are many types of equilibrium and a system is not in thermodynamic
equilibrium unless the conditions of all the relevant types of equilibrium are satisfied
Thermal
equilibrium
20 °C
30 °C
33 °C
35 °C
32 °C
32 °C
32 °C
32 °C
Mechanical
equilibrium
Phase
equilibrium
Chemical
equilibrium
oil
C H8 + O2
water 3
3 CO2 + 4 H2O
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Process and cycles
Any change that a system undergoes from one equilibrium state to another is called a
process, and the series of states through which a system passes during a process is
called the path of the process
paths
Property A
state 4
state 1
state 2
state 3
Property B
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Process and cycles
When a process proceeds in such a manner that the system remains infinitesimally
close to an equilibrium state at all times, it is called a quasistatic, or quasi-equilibrium,
process
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Process and cycles
The prefix iso- is often used to designate a process for which a particular property
remains constant. An isothermal process, for example, is a process during which the
temperature T remains constant; an isobaric process is a process during which the
pressure P remains constant; and an isochoric (or isometric) process is a process
during which the specific volume v remains constant.
Property A
Property B
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
The Steady-Flow Process
The terms steady and uniform are used frequently in engineering, and thus it is
important to have a clear understanding of their meanings. The term steady implies no
change with time. The opposite of steady is unsteady, or transient. The term “uniform”,
however, implies no change with location over a specified region
27 °C
22 °C
Control volume
25 °C
mcV = const.
EcV = const.
Mass in
29 °C
20 °C
Mass out
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Temperature
Several properties of materials change with temperature in a repeatable and
predictable way and this forms the basis for accurate temperature measurement
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Temperature. Zeroth principle
At equilibrium, heat transfer stops, and the two bodies are said to have reached
thermal equilibrium. The equality of temperature is the only requirement for thermal
equilibrium. If two bodies are in thermal equilibrium with a third body, they are also in
thermal equilibrium with each other
100 °C
20 °C
60 °C
60 °C
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Exercises!
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Thermodynamics
Why does a car pick up speed on a downhill road even when it is not using the
engine? Does this violate the conservation of energy principle?
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Thermodynamics
A friends of yours states that a cup of cold tee on his table warmed up to 50°C by
picking up energy from the surrounding air, which is at 20°C. Is there any truth to his
claim? Does this process violate any thermodynamic laws??
Conservation of energy: during an interaction, energy can change from one form to
another but the total amount of energy remains constant
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Thermodynamics
A large fraction of the thermal energy generated in the engine of a car is rejected to
the air by the radiator through the circulating water. Should the radiator be analyzed
as a closed system or as an open system?
T1
Mass out
T2
T3
Mass in
T5
T4
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Thermodynamics
A friends of yours ask you to get a can of soft drink from the fridge. He put it into the
refrigerator so that it would cool. Would you model the can of soft drink as a closed
system or as an open system?
mass
Closed
system
energy
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Thermodynamics
What is the difference between intensive and extensive properties?
extensive
m
m½ m
½m
V
V½ V
½V
T
T
T
T
P
P
P
P
ρ
ρ
ρ
ρ
intensive
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Thermodynamics
For a system to be in thermodynamic equilibrium, do the temperature and the
pressure have to be the same everywhere?
Thermal
equilibrium
20 °C
30 °C
33 °C
35 °C
32 °C
32 °C
32 °C
32 °C
Mechanical
equilibrium
Phase
equilibrium
Chemical
equilibrium
oil
C H8 + O2
water 3
3 CO2 + 4 H2O
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Thermodynamics
What is a quasi-equilibrium process? What is its importance in engineering?
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Thermodynamics
What is a steady-flow process?
27 °C
22 °C
Control volume
25 °C
mcV = const.
EcV = const.
Mass in
29 °C
20 °C
Mass out
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Thermodynamics
Define the isothermal, isobaric, and isochoric processes
What is the zeroth law of thermodynamics?
100 °C
20 °C
60 °C
60 °C
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
First law of thermodynamics
Marco Caniato
Free University of Bozen
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
First law of thermodynamics
The first law of thermodynamics, also known as the conservation of energy principle,
provides a sound basis for studying the relationships among the various forms of
energy and energy interactions
The first law of thermodynamics states that energy can be neither created nor
destroyed during a process; it can only change forms
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
First law of thermodynamics
For all adiabatic processes between two specified states of a closed system, the net
work done is the same regardless of the nature of the closed system and the details of
the process
Chemical work
Mechanical work
Electrical work
Nuclear work
Elastic work
…
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
First law of thermodynamics
A major consequence of the first law is the existence and the definition of the property
total energy E.
Change in the
p
property of the
1
system
Pi
Pf
2
Vi
Vf
V
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
First law of thermodynamics
Consider some processes that involve heat transfer but no work interactions. The
boiled egg is a good example for this case
2J
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
First law of thermodynamics
Consider some processes that involve heat transfer but no work interactions. The
water boiling is a good example for this case
1kJ
20 k J
NET HEAT TRANSFER = 19 kJ
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
First law of thermodynamics
Now consider a well-insulated (i.e., adiabatic) room heated by an electric heater as
system
Win = 8 kJ
∆E = 8 kJ
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
First law of thermodynamics
The conservation of energy principle again requires that the increase in the energy of
the system be equal to the boundary work done on the system.
Win = 8 kJ
∆E = 8 kJ
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Energy balance
The conservation principle can be rewritten as follows: The net change (increase or
decrease) in the total energy of the system during a process is equal to the difference
between the total energy entering and the total energy leaving the system during that
process
Ein - Eout = ∆ Esystem
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Energy balance
The determination of the energy change of a system during a process involves the
evaluation of the energy of the system at the beginning and at the end of the process,
and taking their difference.
Efinal - Einitial = E2 – E1 = Ein - Eout = ∆ Esystem
stationary
∆ Usystem = ∆ Esystem
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Mechanisms of Energy Transfer
Energy can be transferred to or from a system in three forms: heat, work, and mass
flow. Energy interactions are recognized at the system boundary as they cross it, and
they represent the energy gained or lost by a system during a process.
Heat
molecular movement and storage
Work
not driven by temperature
Mass flow
movement of mass in an open system
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Mechanisms of Energy Transfer
Energy can be transferred in the forms of heat, work, and mass, and that the net
transfer of a quantity is equal to the difference between the amounts transferred in
and out, the energy balance can be written more explicitly
∆ Esystem = (Qin – Qout ) + (Win – Wout ) + (Efinal - Einitial)
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Mechanisms of Energy Transfer
For a closed system undergoing a cycle, the initial and final states are identical, and
thus
∆ Esystem = 0
p
W=Q
V
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Mechanisms of Energy Transfer
Example: mixing hot water in a pan
Qout = 250 kJ
Win = 100 kJ
Q = 600 kJ
Determine the final internal energy
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Energy balance
Example: mixing hot water in a pan
Efinal - Einitial = E2 – E1 = Ein - Eout = ∆ Esystem
stationary
∆ Usystem = ∆ Esystem
U2 – U1 = Ein - Eout
U2 – U1 = Win - Qout
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Energy balance
Example: mixing hot water in a pan
U2 – U1 = Win - Qout
U2 – 600 = 100 - 250
U2 = 100 – 250 + 600
U2 = 450 kJ
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Mechanisms of Energy Transfer
Example: moving fan
Win = 18 W
Determine the final air velocity
.
m = 0.2 kg/s
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Energy balance
Example: moving fan
Efinal - Einitial = E2 – E1 = Ein - Eout = dEsystem
.
.
Efinal - Einitial
.
Win,electric
stationary
.
.
.
.
= E2 – E1 = Ein - Eout = 0
.
.
= m Ekinetic,out = m v2 / 2
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Energy balance
Example: moving fan
=
,
=
· .
= 6.7 m/s
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Energy balance
Example: light in an office: fluorescent and led
40 lamps, 10 hours,
40 lamps, 10 hours,
60 W, 320 days/years
20 W, 320 days/years
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Energy balance
Example: light in an office: fluorescent and LED
Efinal - Einitial = E2 – E1 = Ein - Eout = ∆Esystem
Win,electric,fluo = 60 x 40 x 10 x 320 = 7680 kW
Win,electric,LED = 20 x 40 x 10 x 320 = 2560 kW
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Efficiency
Performance or efficiency, in general, can be expressed in terms of the desired output
and the required input
= η=
" #$ % &' &'
( )&$ % $ &'
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Efficiency
Example: Water heater
Heat losses = 10 %
η = 100%
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Efficiency
Example: Water heater
Heat losses = 6 %
η = 100%
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Efficiency
Example: Water heater
η = 55%
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Efficiency
the efficiency of equipment that involves the combustion of a fuel is based on the
heating value of the fuel, which is the amount of heat released when a unit amount of
fuel at room temperature is completely burned and the combustion products are cooled
to the room temperature
Combustion gases
*
=
+,
21500 kJ/kg
air
1 kg propane room
temperature
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Efficiency
Most fuels contain hydrogen, which forms water when burned, and the heating value
of a fuel will be different, depending on whether the water in combustion products is in
the liquid or vapor form
C3H8 + O2
Low heating value
3 CO2 + 4 H2O + HEAT!
high heating value
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Efficiency
Example : gas heat generator.
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Efficiency
Example: electrical generator.
A generator is a device that converts mechanical energy to electrical energy, and the
effectiveness of a generator is characterized by the generator efficiency, which is the
ratio of the electrical power output to the mechanical power input
=
-
. / 0 1
234 56 731345
4
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Efficiency
Example: lighting.
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Efficiency of mechanical and electrical devices
The transfer of mechanical energy is usually accomplished by a rotating shaft, and
thus mechanical work is often referred to as shaft work. A pump or a fan receives
shaft work (usually from an electric motor) and transfers it to the fluid as mechanical
energy.
3-2
=
89 :,;<
89 :,
=
89 :, =8 ;>>
89 :,
= 1-
8 ;>>
89 :,
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Efficiency of mechanical and electrical devices
Example: rotating shaft
3-2
=
? ℎ
$ ℎ A
BC $
D 3-2,01
#
'ℎ
A&$%
∆D ℎ A&$%
=
F #ℎ ' $
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Efficiency of mechanical and electrical devices
Example: turbine
3-2
=
? ℎ
$ ℎ A
D 3-2,
BC $
#
'ℎ
F #ℎ
=
A&$% ∆D
' &'
ℎ A&$%
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Efficiency of mechanical and electrical devices
Example: rotating shaft
3-2
=
G3-2510-256 31347H 01-435/3 I 23 I6 0J
89 :,
=
· KL⁄
N O34
504
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Efficiency of mechanical and electrical devices
motor efficiency and generator efficiency should not be confused with mechanical
efficiency
3-2 = P
P
4
3-2 =
4.013 731345 4
motor
fan
generator
turbine
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Efficiency of mechanical and electrical devices
Example: hydraulic turbine generator
turbine
Water flow 3500 kg/s
30 m
Generator 836 kW and η=0.94
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Efficiency of mechanical and electrical devices
Example: hydraulic turbine generator
0
.
∆D =
.
NL =NQ
R
+
KLL =KQL
0
0
+B T −T
∆D = 30 · 9.81 · 3500 = 1,03 ?F = 1030 ^F
K34566
=
4.013=731345
4
=
VW
V
= 0.811
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Efficiency of mechanical and electrical devices
Example: hydraulic turbine generator
4.013
=
< _
a
3-2
.
=
`a
b ;
=
b ;
89 :,;<
89 :,
=
.
.cd
= 0.85
>:be
.
8
F/25I = 0.8 · 1030 = 824 kW
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 1
It is assumed that a person at rest transfers an average heat output of 100 W to the
environment and that in a theatre containing 1800 people, the air conditioning system
stops to function. Let’s assume that the external walls of the theatre are adiabatic.
1.Calculate the internal energy variation of the air in the theatre after 15.0 minutes.
2.Which is the internal energy variation for the system containing air and people?
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 1
Calculate the internal energy variation of the air in the theatre after 15.0 minutes.
system=air
The variation in internal energy is calculated by applying the First Principle of
Thermodynamics
∆U = Q - L
where L = 0 because the walls of the system are rigid and non-deformable, so there is
no change in volume
∆U = Q
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 1
Q is the heat that a person exchanges with the surrounding environment, due to
physiological mechanisms and mechanical activity, and its value depends on the type
of activity (sedentary or moving).
P = Q / ∆t
So the total exchanged heat is
Seconds!!!
Q = P ∆t
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 1
Take into account the number of present people!
Q = 100W 900s 1800 people
Q = 100W 900s 1800 people = 162 MJ
Thus
∆U = Q = 162 MJ
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 1
Which is the internal energy variation for the system containing air and people.
system=air + theatre
L = 0 because the boundaries of the system are rigid and non-deformable, so there is
no change in volume
Q = 0 because the boundaries of the system are adiabatic, so there is no heat
exchange
∆U = 0
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 2
A closed container with rigid and fixed walls contains 700 liters of water in a liquid
state at a temperature of 40°C. A cylindrical metal body (diameter D = 45 cm and
height H = 55 cm) is subsequently immersed in the container at a temperature of
95°C, with a density of 4000 kg/m3 and specific heat 500 J/ kg K. Determine the
temperature of the water and the metal at equilibrium, assuming that the heat
dispersed to the external environment is not taken into account. It should be
remembered that for water the density is 1000 kg/m3 and the specific heat is 4.2 kJ/
kg K. Let’s assume that the container is insulated both thermally and mechanically.
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 2
Applying the First Principle of Thermodynamics to the whole system (water + metal)
and considering that the tank walls (system boundary) are adiabatic and fixed,
∆U = Q – L = 0
Therefore, using the additive property of the internal energy (the internal energy of the
system is equal to the sum of the internal energies of its components):
∆U = ∆Uwater + ∆Umetal = 0
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 2
1000 *700 * 4.2 * (te - 40)+ 4000* h ∗ + ∗ (" ⁄2) *0.5 (te – 95) = 0
te = 43.1 °C
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 3
Let us consider a thermally insulated container, so that we can suppose that the heat
exchange between system and environment is null (Q = 0): in this way the
phenomena at the edges are neglected. The container contains 100 l of H2O agitated
by a propeller connected to an electric motor. Consider that the transformation takes
place under conditions of constant pressure and P= 368 W be the power supplied by
the engine and t = 20 min is be the time for which the engine is kept in operation.
Determine the ∆ U internal energy variation of the system. Moreover, knowing that the
specific heat of the water is cp= 4.2 kJ/ kg K at atmospheric pressure, and that the
initial temperature of the system is Tin = 20°C, calculate the final temperature (Te) at
the end of mixing.
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 3
∆U = Q – L
No variation in temperature, no heating added and/or exchanged
∆U = – L
∆U = – L = – P * dt = 368 W * 20 min * 60 = 441.6 KJ
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 3
m3 = m01 +
∆n
P
lm
l'
∆U =
P
∆U =
P (m3
= 293.15 +
− m01 )
441600
= 294.2 p
4200 ∗ 100
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Mechanisms of heat transfer
Part 1
Marco Caniato
Free University of Bozen
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Mechanisms of heat transfer
Heat can be transferred in three different ways: conduction, convection, and radiation
2J
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction
Conduction is the transfer of energy from the more energetic particles of a substance
to the adjacent less energetic ones as a result of interactions between the particles
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction
Conduction is verified when there is no thermal equilibrium
⃗=−
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction
λ is defined as thermal conductivity of a material
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction
thermal conductivity - fluids
=
general
=
fluids
Reference parameter
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction
λ is defined as thermal conductivity of a material
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction
thermal conductivity - solids
phonons
=
solids
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction
General equation
= T (x,y,z,t)
⃗=−
( , , , )
0
−
=
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction
General equation
0
+
Variation of ⃗ in space and time
⃗=−
=
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction
General equation
0
=−
Thermal inertia
-5 °C
+20 °C
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction
General equation
0 =−
0
0
+
+
=0
y
x
z
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction
General equation
=0
=
+!
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction
Determining A e B constants
T
"
0 =
T2= +20
0
" °C
T1= 0 °C
z
0+!
=!
=
+!
=
+
"
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction
Determining A e B constants
"
0 =!
=
+
"
"
=!
−
= −# $
"
"
=
−− " "
=!
− "
=
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction
Propagation path for monodimensional case
T
= −#
−
"
T2= +20 °C
T1= 0 °C
z
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction
Propagation path for monodimensional case. Multilayer
=−
T
Ti Ti
Ti+1 Ti+1
λn
λ2
Tn+1
z
=−
λ1
=−
"
−
"
−
&
Tn
%
−
'"
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction
Propagation path for monodimensional case. Multilayer
= −(
T
*+"
1
*
(
−
'" )
*
Tn
Ti
λn
Tn+1
Ti+1
λ2
λ1
z
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Mechanisms of heat transfer
Part 2
Marco Caniato
Free University of Bozen
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Mechanisms of heat transfer: convection
Convection is the mode of energy transfer between a solid surface and the adjacent
liquid or gas that is in motion and it involves the combined effects of conduction and
fluid motion.
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection
Convection is called forced convection if the fluid is forced to flow in a tube or over a
surface by external means. In contrast, convection is called free (or natural)
convection if the fluid motion is caused by buoyancy forces induced by density
differences due to the variation of temperature in the fluid
2J
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection
Convection can be considered including a fluid without phase-change (single-phase
outflow convection) or phase change, such as condensation and vaporization.
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection
it is useful to distinguish between flow regimes. The laminar regime and turbulent
regime
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection
In the heat exchange with the limiting surface, it has a great relevance to precisely
know the layer of fluid closest to it, i.e. the boundary layer
tp
h
tf
w
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection
Let’s proceed to analyze the Newton law. Boundary condition
x
Tp
Tf
=
=
(
−
)
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection
How to determine α?
The knowledge of the temperature field in the fluid is a prerequisite for the calculation
of the convection coefficient. This can only be determined from the velocity field.
General dimensional empirical approach!
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection
Let’s assume that the convection coefficient is a function of n quantities
=
………..
=
15625 separate tests!!!!
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection
Similarity theory or dimensional analysis
=
………..
=
………..
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection
Monomial multiplication: dimensionless group
(-2ab) x (5a2) x (3ab2)
∏
=
· ……… ·
!
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection
By defining the n quantities in terms of their relationship with the m fundamental
quantities it is possible to write
"
∏
= #
∏
=#
$
$
=#
$%
·. . .·
$%'
#&
· ……… ·
$ '
#&
* ….* $!
· … … … · #& '
!
( = 1, . . ., n
· ……… · #
$
$!
· ……… ·
* ….* $!' !
$!'
#&
!
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection
Dimensionless condition
+
+
&
… +
…
… +
&
ℎ
· …
ℎ
0
= …
0
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection
Buckingham theory: if there is a physically meaningful equation involving a certain
number n of physical variables, then the original equation can be rewritten in terms of
a set of p = n − k dimensionless parameters constructed from the original variables.
T
L
.1
.2
M
.3
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Mechanisms of heat transfer: convection
Based on the theoretical model of the phenomenon, also confirmed by extensive
experimental evidence, the convection coefficient is dependent on:
tp
h
tf
w
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection
Convection coefficient can be expressed as:
=
∏
=#
∏
=8
$
1, 3, 4, 5, 6 , 7
* ….* $!
·3
9
·7
!
:
· ……… ·
·1
;
·4
<
$ '
#&
·5
=
·
* ….* $!' !
>
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection
The fundamental quantities on which the considered quantities depend are the length
L, the mass M, the time t, and the temperature T
8
L
M
t
T
3
0
1
1
0
−3 −1
1
0
7
2
0
−2
1
1 4
1
0
0
0
−3
1
0
0
5
−1 1
1
1
−1 −3
0 −1
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection
Dimensionless multiplication
0
1
1
0
−3 −1
1
0
2
0
−2
1
.
1
0
0
0
−3
1
0
0
−1 1
1
1
−1 −3
0 −1
ℎ
ℎ?
ℎ@
ℎA
ℎB
ℎC
ℎD
=
0
0
0
0
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection
Dimensionless multiplication
ℎ? + 2ℎ@ + ℎA − 3ℎB − ℎC + ℎD = 0
ℎ + ℎB + ℎC + ℎD = 0
−3ℎ − ℎ? − 2ℎ@ − ℎC − 3ℎD = 0
− ℎ − ℎ@ − ℎD = 0
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection
Given the rank of the matrix, which is equal to 4, the values of three of the hi variables
can be set arbitrarily, the remaining four stay non-dependent .
0
0
ℎ? + 2ℎ@ + ℎA − 3ℎB − ℎC + ℎD = 0
1
ℎ + ℎB + ℎC + ℎD = 0
1
0
1
0
0
−3ℎ − ℎ? − 2ℎ@ − ℎC − 3ℎD = 0
− ℎ − ℎ@ − ℎD = 0
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection
Given the rank of the matrix, which is equal to 4, the values of three of the hi variables
can be set arbitrarily, the remaining four stay non-dependent .
0 + 0 + ℎA − 3ℎB − ℎC + ℎD = 0
ℎA − 3ℎB − 0 − 1 = 0
ℎA = 1
1 + ℎB + ℎC + ℎD = 0
1 + ℎB + 0 − 1 = 0
ℎB = 0
−3 − 0 − 0 − ℎC − 3ℎD = 0
ℎC = 3 − 3
ℎC = 0
−1 − 0 − ℎD = 0
ℎD =-1
ℎD =-1
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection
three dimensional products are obtained whose exponents result from the three
solutions identified
Π1
Π2
Π3
ℎ
1
0
0
ℎ?
0
1
0
ℎ@
0
0
1
ℎA
1
1
0
ℎB
0
1
0
ℎC ℎ D
0 −1
−1 0
1 −1
=
?
@
81
314
=
5
=
7 5
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Forced convection
In conclusion, Buckingham's theorem allows us to replace the analysis of the general
function with the dimensional one
=
1, 3, 4, 5, 6 , 7
F=
GH, IJ
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Forced convection: examples
Some empirical relations
F = K GH $ IJ L
F = 0.332 GH M.B IJ M.@@
F = 0.0296 GH M.P IJ M.@@
………
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Natural convection
Some empirical relations
Thermal dilatation
=
1, Q · R · ∆T, 4, 5, 6 , 7
As before
=
81
?
4? Q R ∆T U@
=
5?
@
=
7 5
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Natural convection: examples
Some empirical relations
F = V #J & IJ &
G+ = #J IJ
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction plus convection
W T=f,e 6 X ( ? −Tf,i )
Tp
W = 6 X ( ?− )
( Y− ")
W=
GZ[Z
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction plus convection
( Y− ")
W=
GZ[Z
( Y− ")
W=
1
\
1
+
+
X
YX
"X
X( Y − " )
W=
1
\ 1
+ +
Y
"
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Mechanisms of heat transfer
Part 4
Marco Caniato
Free University of Bozen
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Mechanisms of heat transfer: radiation
Radiation is the energy emitted by matter in the form of electromagnetic waves (or
photons) as a result of the changes in the electronic configurations of the atoms or
molecules
2J
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Radiation
Radiation is a volumetric phenomenon and all solids, liquids and gases emits,
absorbs, or transmits radiation of varying degrees
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Radiation
Focus on electromagnetic waves
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Radiation
Electromagnetic waves can be imagined as a self-propagating transverse oscillating
wave of electric and magnetic fields. A plane linearly polarized wave propagating from
left to right. The electric and magnetic fields in such a wave are in-phase with each
other, reaching minima and maxima together
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Radiation
The radiation impinging a system is generally divided into three components: a
certain amount is absorbed, another is reflected and the remaining part is transmitted
through the system.
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Radiation
In opaque systems, the transmitted part is negligible and the thermal radiation can be
analysed as a surface phenomenon.
Black surface
(black body)
J
J
Gr
G
E
G
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Radiation
Specific frequency behavior. Example: traditional glass
τ
0.9
0.1
1µm
λ
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Radiation
The maximum rate of radiation that can be emitted from a surface at an absolute
temperature Ts is given by the Stefan–Boltzmann law as (heat flux rate) for black
body:
=
= 5.67 · 10
A is the surface area
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Radiation
What is a black body?
- no body at a certain temperature can emit at a certain date wavelength plus energy
of a black body at the same temperature
- a black body absorbs all of the incident energy regardless of the wavelength and
direction
- the emission intensity is independent of direction (diffuse emission) (Lambert’s laws)
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Radiation
Plank’s law correlates monochromatic emission intensity and monochromatic
emission to wavelength and temperature.
=
1
−1
Black body
3.742
10 %
$
⁄
= 1.439 10 %
⁄
=
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Radiation
Wien's displacement law states that the black-body radiation curve for different
temperatures will peak at different wavelengths that are inversely proportional to the
temperature.
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Radiation
Example: greenhouse effect
6000 °K
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Radiation
Example: greenhouse effect
λ
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
radiation
Black body / grey body: focus
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
radiation
Prevost's law defines in a simple way the energy that is exchanged by radiation
black body
(
=
)
−
*
=+
grey body
=+
,
= +( , )
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
radiation
General law for radiation: black body
a1 = 1
a2 = 1
=
T1 > T2
(
-
)
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
radiation
General law for radiation: grey body
a1 ≠ 1
a2 ≠ 1
=
T1 > T2
(
−
1
1
+
−1
+
+
)
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
radiation
General law for radiation: EXAMPLE of grey bodies
a1 = 0.1
a2 = 0.1
=
300°K > 270°K
(
−
1
1
+
−1
+
+
)
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
radiation
General law for radiation: EXAMPLE of grey bodies
a1 = 0.1
a2 = 0.1
10 · 5.67 · 10 (300 − 270 )
=
1
1
+
−1
0.1
0.1
300°K > 270°K
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
radiation
General law for radiation: EXAMPLE of grey bodies
a1 = 0.1
a2 = 0.1
0.9
0.9
0 0
= 83 W
0 3
300°K > 270°K
3 3
= 156 W
= 1292 W
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
radiation
General law for radiation
= 4(+ , +
= 4 + ,+
= 4 + ,+
, )(
,
,
,
,
,
−
)
+
(
+
(
Cost?
−
+
)
)
−
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
radiation
General law for radiation
T1 = 300 K
T2 = 270 k
+
+
= 163470
−
≅
T1 = 330 K
= 30 K
x2
T2 = 270 k
+
+
= 182470 K
−
= 60 K
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
radiation
General law for radiation
= 4 + ,+
,
,
(
+
=+
5
+
−
)
−
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Global mechanism of heat transfer
rad
rad
conv
89;
=<
)
−
0
conv
cond
*67
rad
rad
Te
Ti
= +*67
897 =
:
)
−
) −
0
0
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
radiation
General law for radiation
)
=<
)
= <)
0
=<
0
= <0
)
)
)
)
−
0
−
−
−
+ +*67
)
−
+ +*67
)
−
0
0
0
0
0
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
radiation
Example: radiation from a person
19 °C
89;
= 6 · 1.3 · 28 − 19
*67 = · · 1.3 · 301 − 292
28 °C
=8=
= 70.2 + 65.7 = 135.9 W
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Lecture 5. Mechanisms of heat transfer
Part 8. Exercises
Marco Caniato
Free University of Bozen
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction:
A flat wall consists of three layers in series of bricks 15 cm thick, concrete 10 cm thick
and plaster 2 cm thick respectively. The temperature of the outer face of the brick wall
is 25 °C and the temperature of the outer face of the plaster is 5 °C. Consider the
thermal conductivity of bricks, concrete and plaster of 0.70, 1.6 and 1.0 W/mK
respectively. The specific heat flow and temperature of the brick-concrete wall
interface is to be evaluated.
25 °C
5 °C
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction:
1
=
+
−
+
1
=
25 − 5
0.15 0.1 0.02
+
+
0.7 1.6 1.0
= 67.4
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction:
In order to evaluate the temperature of the T1-2 brick-concrete wall interface we
consider the heat flow transmitted by conduction only through the brick layer:
=
1
25 −
stationary
= 67.4
=
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Conduction:
In order to evaluate the temperature of the T1-2 brick-concrete wall interface we
consider the heat flow transmitted by conduction only through the brick layer:
1
67.4 =
25 −
0.7
0.15
= 10.5 °!
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection:
A pipe with an inner diameter D = 30 mm and a length of L = 1 m is run through by
water at the average temperature Tf = 90 °C. If the water velocity is u = 1 cm/s and the
wall temperature Tp = 40 °C, determine the heat flow given to the wall by convection.
For the evaluation of the water-tube convective heat exchange coefficient, use the
following heat exchange correlation:
)
"# = 1.86 %& Pr
*
+.
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection:
Temperature
K
Thermal
Density Specific heat conductivity
kg/m3 ρ cp J/kg °C
λ W/m °C
Dynamic
Thermal
diffusivity m2/s α diffusivity
kg/m2 µ
90 °C
40 °C
cinematic
diffusivity m2/s γ
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection:
, =-ℎ
/
−
0
"# · 2
=)
)
1.86 %& Pr
*
,=)
/
−
−
0
+.
·
/
0
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection:
3 ·# ·)
%& =
4
56 =
9 :
=
/
−
2
0
78 · 4
= 65 °! = 338.15 <
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection:
9 :
=
/
−
2
0
= 65 °! = 338.15 <
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection:
Linear interpolation:
>+ − > = − =
=+ =
> −>
>
=
>+
=+
>
=
+=
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection:
Linear interpolation:
=+,@
338.15 − 320 980 − 989
=
+ 989
340 − 320
=+,@ = 980.83
=+,B = ⋯
=+, = ⋯
=+,D = ⋯
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection:
3 ·# ·)
%& =
= 695
4
56 =
E ·4
= 2.69 ∗ 10
)
"# = 1.86 %& Pr
*
+
+.
= 7.02
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Convection:
= ℎ= ℎG)*
/
−
/
0
−
"# · 2
=)
0
"# · 2
=)
= 726.6
/
−
0
/
−
0
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Radiation:
A black body is at a constant temperature of 300 °C. Evaluate the specific heat flux
emitted by radiation.
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Radiation:
= H+
I
= 5.67 · 10
J
· 300 + 273.15
4
= 6118
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
200 °C
50 °C
→L
H+ I − LI
=
1
1
+
−1
M
ML
=
stationary
L→
H+ LI − I
=
1
1
+
−1
M
ML
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
H+ I − LI
H+ LI − LI
=
1
1
1
1
+
−1
+
−1
M
M
ML
ML
1
1
1
1
I
I
+
−1
− L −
+
−1
M
ML
M
ML
1
1
1
1
+
−1
+
−1
M
ML
M
ML
I
L
−
I
=0
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
1
1
1
1
I
I
+
−1
− L −
+
−1
M
ML
M
ML
1
1
1
1
+
−1
+
−1
M
ML
M
ML
All constant – No variables
:N
+
:O
−1
I
L
−
I
=0
:P
+
:O
−1 =k
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
1
1
+
−1
M
ML
1
1
+
−1
M
ML
1
1
+
−1
M
ML
I
I
−
−
I
I
L
−
I
L
I
L
1
1
−
+
−1
M
ML
Q
1
1
−
+
−1
M
ML
Q
1
1
−
+
−1
M
ML
I
L
I
−
=0
I
L
−
I
Q =0·Q
I
L
−
I
=0
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
I
1
1
+
−1 −
M
ML
I
1
1
+
−1 +
M
ML
I
1
1
+
−1 −
M
ML
I
L
I
1
1
+
−1 =
M
ML
1
1
+
−1 +
M
ML
I
I
L
=
I
L
I
1
1
+
−1 +
M
ML
I
L
I
1
1
+
−1 +
M
ML
1
1
+
−1 =
M
ML
I
L
1
1
+
−1 =0
M
ML
I
L
1
1
+
−1
M
ML
1
2
1
+
+ −2
M
ML M
1
1
1
1
+
−1 + I
+
−1
ML
ML
M
M
1
2
1
+
+ −2
M
ML M
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
I
I
L
=
1
1
1
1
+
−1 + I
+
−1
M
M
ML
ML
1
2
1
+
+ −2
M
ML M
Remember: use Kelvin!!!!!!
R
L
=
473.15I
1
1
1
1
+
− 1 +323.15I
+
−1
0.1 0.1
0.1 0.1
= 417.9 <
1
2
1
+
+
−2
0.1 0.1 0.1
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Absence of intermediate plane:
200 °C
→
50 °C
→
=
- · H+ I − I
=
1
1
+
−1
M
M
473.15I − 323.15I
1
1
+
−1
0.1
0.1
5.67 · 10
J
= 117
S
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
presence of intermediate plane:
200 °C
→L
50 °C
→L
=
L→
Heat fluxes are the same so it is the same
to compute the first or the second one
H+ I − LI
H+ LI − I
=
=
=
1
1
1
1
+
−1
+
−1
M
ML
ML M
L→
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
presence of intermediate plane:
200 °C
→L
=
L→
50 °C
→
=
473.15I − 417.19I
1
1
+
−1
0.1
0.1
5.67 · 10
J
= 58.5
S
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
The ideal gas
Marco Caniato
Free University of Bozen
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Pure substances
A substance that has a fixed chemical composition throughout is called a pure
substance
N2
Air
vapour
air
oil
water
Liquid air
water
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Pure substances
There are many practical situations where two phases of a pure substance coexist in
equilibrium.
State 1
State 2
P= 1 atm
P= 1 atm
T
T
Compressed liquid
= 20 °C
= 100 °C
Saturated liquid
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Pure substances
Once boiling starts, the temperature stops rising until the liquid is completely
vaporized
State 3
State 4
P= 1 atm
P= 1 atm
T
T
saturated vapor
Saturated liquid
= 100 °C
= 100 °C
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Pure substances
Once the phase-change process is completed, we are back to a single phase region
again
superheated vapor
State 5
P= 1 atm
T
= 100 °C
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Pure substances
This constant-pressure phase-change process is illustrated on a T-v diagram
Saturation
temperature
Saturated
mixture
Superheated
vapor
Temperature
Compressed
liquid
Volume
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Pure substances
The variations of properties during phase-change processes are best studied and
understood with the help of property diagrams
CRITICAL
POINT
CRITICAL
POINT
P2 = cost
P
Superheated
vapor region
T2 = cost
P= 1 MPa
P1 = cost
T = 150 °C
Saturated
liquid-vapor
region
V
Compressed
liquid region
T
Superheated
vapor region
T1 = cost
Saturated
liquid-vapor
region
V
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Pure substances
the P-T diagram of a pure substance is often called the phase diagram since all three
phases are separated from each other by three lines
Substances
that
expand on freezing
Substances
that
contract on freezing
4 °C
LIQUID
P
V
Triple point
VAPOR
0
4
T [°C]
T
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Entalpy
In the analysis of certain types of processes, particularly in power generation and
refrigeration, we frequently encounter the combination of properties u + Pv. For the
sake of simplicity and convenience, this combination is defined as a new property,
enthalpy, and given the symbol h
u2
P2 V2
u1
P1 V1
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
The ideal-gas equation of state
Any equation that relates the pressure, temperature, and specific volume of a
substance is called an equation of state
PV=RT
Gas constant
R = Ru / M
Molar mass
m=MN
R = kB NA
Same for all substances
Universal Gas Constant
R = 8.3163 J / mol K
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
The ideal-gas equation of state
Determine the mass of the air in a room whose dimensions are 4 m x 5 m x 6 m at 100
kPa and 25 °C. Air molecular weight: 28.9647 kg/kmol
5m
P = 100 kPa
T = 25 °C
m=?
6m
4m
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
The ideal-gas equation of state
V = 4 m * 5 m * 6 m = 120 m3
PV=mRT
R = Ru / M
P V = m Ru T / M
P V = m Ru T / M
m = P V M / Ru T
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
The ideal-gas equation of state
V = 4 m * 5 m * 6 m = 120 m3
100 · 120 · 28.9647
=
= 140.27
25 + 273.15 · (8.3163)
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Processes
Marco Caniato
Free University of Bozen
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Processes
The differential form of the first law equation written for infinitesimal transformations
and in specific terms gives
−
=U
−
m
=U+P +
ρ
−
= U + PV +
H
2
2
+ mgz
+ mgz
When
the fluid
experiences
negligible changes
in its kinetic and
potential energies
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Processes
Passing to differential and unit of mass expressions
−
= u
−
= h
= ! + "# !$
= −%!& + " !$
Only way to produce work in a close
system is to move boundaries and
thus to vary the volume.
Only way to produce work in an
open system is to move the flow
inside the system. The volume will
not vary and the motion is caused
by pressure difference.
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Processes
The equation can be used regardless the system is open or closed!
% = RT
! +!%!&
= "= −
+ %!&
R "dT
# dT
! + %!& = " dT − "# dT
! + "# dT = −%!& + " dT
−
= u
=
−
= h
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Isobaric Processes
The pressure is considerable constant during the process
* = &!% + "# dT = −%!& + " dT
P
1
* = −%!& + " dT = "
2
*
*
v1
v2
V
= &!% =
= −%!& = 0
$ − $,
% − %,
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Isochoric Processes
The volume is considerable constant during the process
* = !% + "# dT = −%!& + " dT
P
* = !% + "# dT
P1
1
*
P2
2
*
V
= "# $ − $,
= &!% = 0
= −%!& = −% & − &,
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Adiabatic Processes
The heat transfer is null during the process
−
= u
= ! + "# !$
−
= −%!& + " !$
-$ !%.%
0 = ! + "# !$
0 = -$
#⁄
#
= h
+
-!$ ,⁄23,
-!$ 1.0 − 1
"
0=
"#
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Adiabatic Processes
The heat transfer is null during the process
!%
1
−$
= !$
%
0−1
!%
1 !$
−
=
%
0−1 $
!%
1
!$
4 −
=
4
%
0
−
1
,
, $
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Adiabatic Processes
The heat transfer is null during the process
%,
1
$
ln =
ln
%
0 − 1 $,
Isothermic
P
1
$
%,
ln = ln
%
$,
P1
P2
2
v1
v2
V
%,
=
%
$
$,
,
23,
,
23,
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Adiabatic Processes
Other expression of adiabatic process
%,
=
%
$
$,
,
23,
,
,
$, 23,
$ 23,
$
= $
&, ,
&
2
2
1 23,
1 23,
$
= $
&, ,
&
,
%, $,23,
=% $
-$
% =
&
,
23,
,
,
-$, 23,
-$ 23,
$,
=
$
&,
&
,
,
1 23,
1 23,
7,
7,
$
= $
&, ,
&
2
&,3, $,23,
=&
2
3, 23,
$
2
&,3, $,23,
23,
2
= &
2
3, 23,
$
23,
2
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Adiabatic Processes
Other expression of adiabatic process
2
&,3, $,23,
,32
&, 2 $,
23,
2
=&
= &
,32
2
$
&
$ =
-
2
3, 23,
$
23,
2
,32
&, 2 &, %,
23,
2 (3,)
&,
$,
=&
,3272
&, 2 %,
,32
2
=&
&%
,3272
2
%
=&
23,
2 (3,)
,32
$, &, 2
$
,32
2 7,
&,
%,
,
&,2 %,
=&
,
2
=& %
,32
2 7,
=$ &
,32
2
%
&, %,2
= & %2
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Polytropic Processes
Polytrophic processes are generally considered to be a generalization of isothermal
and adiabatic processes
&v = cost
isobaric
n=0
isothermal
n=1
isochoric
n→∞
adiabatic
n=k
= ! + "# !$
−
= h
cannot be simplified
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 1
A tank with volume V=58 dm3 contains nitrogen (N2) at a pressure of 1.5 bar and at a
pressure of temperature of 27°C. Nitrogen molecular mass is 28.01 and it is
compressed up to 12 bar and the final volume occupied by gas is 10 dm3. The work
carried out on the compression system is of 10 kJ. Determine the heat exchange and
enthalpy variation. Ru is 8314 J / kg K
compression
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 1
Enthalpy of nitrogen [kJ/kg]
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 1
ℎ = A + -$
SCHEME
Q=? ∆H?
=
ℎ = A +
· ∆A + W ∆A = A − A,
&, ,
=
- $,
-EF =
ℎ, = A, +
%
&
tables
=
-G
HEF
-$
&
$=
-
ℎD depends on temperature
, %,
ℎ, = A, + -$,
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 1
A tank with volume V=58 dm3 contains nitrogen (N2) at a pressure of 1.5 bar and at a
pressure of temperature of 27°C. Nitrogen molar mass is 28.01 u and it is compressed
up to 12 bar and the final volume occupied by gas is 10 dm3. The work carried out on
the compression system is of 10 kJ. Determine the heat exchange and enthalpy
variation. Ru is 8314 J / kg K
-EF
&,
,
=
- $,
8314
O
=
= 296.8
28.01
0P Q
&, ,
=
- $,
1.5 · 10S · 0.058
=
296.8 · (27 + 273.15)
= 0.098 0P
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 1
A tank with volume V=58 dm3 contains nitrogen (N2) at a pressure of 1.5 bar and at a
pressure of temperature of 27°C. Nitrogen molar mass is 28.01 u and it is compressed
up to 12 bar and the final volume occupied by gas is 10 dm3. The work carried out on
the compression system is of 10 kJ. Determine the heat exchange and enthalpy
variation. Ru is 8314 J / kg K
&
=
-$
&
$=
-
12 · 10S · 0.01
= 414 Q
=
296.8 · 0.098
The enthalpy and internal energy values of state 2 now can be inferred
Interpolation on tables
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 1
Linear interpolation:
WV − W, U − U,
UV =
+ U,
W − W,
W,
WV
W
U,
UV
U
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 1
Linear interpolation:
UV,Y
520.4 − 415.7 414 − 400
=
+ 415.7
500 − 400
ℎ = 430.4 0O/0P
A =?
Linear interpolation
h = u + Pv
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 1
A =ℎ −& %
A = ℎ − -$
Volume per unit of
mass not known
Ideal gas law
O
A = 430.4 · 10 − 296.8 ∗ 414 = 307524.8
0P Q
\
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 1
− ^ = A − A,
= A − A, + ^
=
∆_ =
·
10
0O
= 307.5 − 222.7 + −
= −17.63
0.098
0P
= 0.098 · −17.63 = −1.720O
· (ℎ − ℎ, ) ∆_ = 0.098 · (430.4 − 311.8) = 11.6 0O
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 2
A closed system contains 3 kg of air. The system undergoes an adiabatic and
reversible transformation from state 1 (P1=3 bar, T1=100°C) to state 2 (T2=300°C).
Determine the pressure and volume at the end of the transformation, the changes in
enthalpy and internal energy, the work exchanged
P1 = 3 bar
T1= 100 °C
m= 3 kg
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 2
Enthalpy of air [kJ/kg]
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
ℎ = A + -$
Exercise 1
SCHEME
ℎ = A +
W=? ∆H? ∆U?
=
%
· ∆A + W ∆A = A − A,
ℎ, = A, +
adiabatic
V2? P2=?
tables
=
-$
&
, %,
,32
$, &, 2
ℎD depends on temperature
ℎ, = A, + -$,
= $&
,32
2
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 2
,32
$, &, 2
3 · 10
&
S
=
= $&
,32
2
100 + 273.15
300 + 273.15
-$
,32
$, &, 2
$
,VVS
`,a
,VVS
,3 `,a
=
=&
,32
2
2
&, $,,32
2
,32
$
=&
&,
$,
$
= 13.47 · 10S &b = &
3 · 287 · (300 + 273.15)
-$
=
13.47 · 10S
&
= 0.37
\
2
,32
=
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 2
Linear interpolation:
WV − W, U − U,
UV =
+ U,
W − W,
W,
WV
W
U,
UV
U
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 2
Linear interpolation:
UV,Y,
401.8 − 300.6 373.5 − 300
=
+ 300.6
400 − 300
ℎ, = 374.6 0O/0P
A =?
A, =?
ℎ = 580.6 0O/0P
Linear interpolation
h = u + Pv
∆_ =
(ℎ − ℎ, )
∆_ = 618 0O
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 2
A =ℎ −& %
A = ℎ − -$
Volume per unit of
mass not known
A, = ℎ, − &, %,
Ideal gas law
A, = ℎ, − -$,
Volume per unit of
mass not known
A = 416.10O/0P
A, = 267.5 kJ/kg
Ideal gas law
Engineering thermodynamics and heat and mass transfer
Prof. Marco Caniato
Exercise 2
∆e =
∆e =
(A − A, )= 445.8 0O
−
−445.8 0O =
compression
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Second Law of thermodynamics
Marco Caniato
Free University of Bozen
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Second law of thermodynamics
It is common experience that a hot egg left in a cooler room eventually cools off
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Second law of thermodynamics
It is clear from these arguments that processes proceed in a certain direction and not
in the reverse direction
ONE WAY
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Second law of thermodynamics
In the development of the second law of thermodynamics, it is very convenient to
have a hypothetical body with a relatively large thermal energy capacity (mass times
specific heat) that can supply or absorb finite amounts of heat without undergoing any
change in temperature. Such a body is called a thermal energy reservoir
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Second law of thermodynamics
work can easily be converted to other forms of energy, but converting other forms of
energy to work is not that easy.
Win
WQ
outout
Qin
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Second law of thermodynamics
Heat engines differ considerably from one another, but all can be characterized by the
following:
1. They receive heat from a high-temperature source (solar energy, oil furnace,
nuclear reactor, etc.)
2. They convert part of this heat to work (usually in the form of a rotating shaft)
3. They reject the remaining waste heat to a low-temperature sink (the atmosphere,
rivers, etc.).
4. They operate on a cycle.
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Second law of thermodynamics
Heat engines and other cyclic devices usually involve a fluid to and from which heat is
transferred while undergoing a cycle. This fluid is called the working fluid
high
temperature
source
Qin
Heat
engine
Wout
Win
Wnet
Qout
Low
temperature
sink
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Second law of thermodynamics
Thermal efficiency: Qout represents the magnitude of the energy wasted in order to
complete the cycle. But Qout is never zero
ℎ
=
η=
η=1−
ℎ
,
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Second law of thermodynamics
Kelvin-Plank Statement: It is impossible for any device that operates on a cycle to
receive heat from a single reservoir and produce a net amount of work.
Thermal
energy
reservoir
Qin =100 KJ
Heat
engine
Wnet =100 KJ
Qout = 0 J
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Second law of thermodynamics
Refrigerators and heat pumps. Refrigerators, like heat engines, are cyclic devices.
The working fluid used in the refrigeration cycle is called a refrigerant.
Warm
environment
TH>TL
QH
evaporator
compressor
engine
condenser
Required input
Wnet
QL
Desired output
Cold
refrigerated
space
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Second law of thermodynamics
Performance. The efficiency of a refrigerator is expressed in terms of the coefficient of
performance (COP).
& '
"#$% =
( )
"#$% =
,
=
&
&
+
,
*
−
+
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Acoustics
1
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
What is Sound?
2
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
What is Sound?
3
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
What is Sound?
4
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
What is Sound?
R = 287
c0
λ=
f
c0 =
( J / kgK )
γ ⋅ R ⋅T
γ = 1 . 41
T = t + 273 ( K )
5
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
What is Sound?
Lp = 10 log p2/prif2 = 20 log p/prif (dB)
Lv = 10 log v2/vrif2 = 20 log v/vrif
LI = 10 log I/Irif
Leq ,T
1
= 10 log 
 T
T

0
p 2 (t ) 
dt 
prif2

(dB)
prif = 20 µPa
(dB) vrif = 50 nm/s.
Irif = 10-12 W/m2.
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Level sum:
What is Sound?
Lp1 = 10 log (p1/prif)2
(p1/prif)2 = 10 Lp1/10
Lp2 = 10 log (p2/prif)2
(p2/prif)2 = 10 Lp2/10
(pT/prif)2 = (p1/prif)2 + (p2/prif)2 = 10 Lp1/10 + 10 Lp2/10
LpT = Lp1 + Lp2 = 10 log (pT/prif)2 = 10 log (10 Lp1/10 + 10 Lp2/10 )
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
What is Sound?
• Example 1:
L1 = 80 dB
L2 = 85 dB
LT= ?
LT = 10 log (1080/10 + 1085/10) = 86.2 dB.
• Example 2:
L1 = 80 dB
L2 = 80 dB
LT = 10 log (1080/10 + 1080/10) =
= 10 log (2* 10 80/10)
= 10 log (2) + 10 log (10 80/10)
= 10 log (2) + 10 * 80 / 10 =
LT = 80 + 10 log 2 = 83 dB.
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
What is Sound?
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
What is Sound?
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
What is Sound?
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Sound insulation
outside noise
airborne noise
Plant vibrations
Impact noise
12
Sound insulation & Sound absorption
absorption, reflection and transmission coefficients
Energy balance equation for a wave impacting a surface:
•
Ei = Er + Ea + Et
Ei = incident sound energy,
Er = reflected sound energy
Ea = absorbing sound energy (converted into heat)
Et = transmitted sound energy
Engineering Thermodynamics and Heat Transfer
Prof. Marco Caniato
Sound-absorbing systems are used for the acoustic treatment
of rooms when it is necessary to reduce reverberated sound
energy.
Their use allows you to control the reverberation time
parameter and the total sound pressure level in the room.
The physical principle behind sound absorption is the
conversion of part of the incident sound energy into heat
14
Sound insulation & Sound absorption
Direct waves come from the source and reach the listener directly, as if he
were in a free field.
Reflected waves are produced by all reflections on the walls enclosing the
room.
The part of energy reflected from room surfaces depends on their acoustic
behavior, in particular on the absorption, reflection and transmission
coefficients (a,r and t).
Sound insulation & Sound absorption
Ea
a=
Ei
Er
r=
Ei
Difference between a sound-insulating
and a sound-absorbing material:
Sound insulating material:
is useful to minimize the transmitted
sound energy “Et”.
Sound absorbing material:
is useful to minimize the reflected
sound energy “Er”.
Et
t=
Ei
Sound insulation & Sound absorption
Ea
a=
Ei
Er
r=
Ei
Et
t=
Ei
Apparent sound absorption coefficient
Er
α = 1− r = a + t = 1−
Ei
Sound Reduction Index
 Ei 
1
R = 10 ⋅ log   = 10 ⋅ log  
t 
 Et 
t=0.01 (1 %)  R=20 dB
t=0.001 (0,1%)  R=30 dB
t=0.00001 (0,0001%)  R=50 dB
Sound Insulating Materials
The “mass law” in acoustics is the base of air-borne sound insulation:
 Ei 
1
R = 10 ⋅ log   = 10 ⋅ log  
t 
 Et 
• Stiffness Controlled Region: R
drops by 6 dB/octave.
•Resonant Frequencies (natural
resonant frequencies specific of each
panel).
• Mass Controlled Region:
R increases by 6 dB/octave.
• Critical
Frequency
and
Coincidence
(the
effect
of
coincidence reduces the sound
insulation proprieties of the panel).
Sound Insulating Materials
Different structures have different “mass law” frequency behaviour:
1
2
Sound absorbing materials and structures
Reverberation Time
Er
α = 1− r = a + t = 1−
Ei
Er
r=
Ei
S’
S1
S
Direct sound
R
S
R
Reflected sound
(method of image sources)
Sound absorbing materials and structures
Reverberation Time
L (dB)
t [s]
V = volume of the room [m3]
TR = 0.16 ⋅
V
 (α ⋅ S )
i
i
i
[s]
Si = surface of i-element [m2]
αi = apparent sound absorption coefficient of i-element
A= α S
equivalent absorption surface [m2]
Sound absorbing materials and structures
Sound level attenuation“∆L” in an enclosed space :
∆L (f) = 10 log (A2/ A1)
A 1 = α1 S
A 2 = α2 S
(dB)
equivalent absorption surface without sound absorbing elements [m2]
equivalent absorption surface with sound absorbing elements [m2].
Sound absorbing materials and structures
ISO 354:2003 specifies a method of measuring the sound absorption
coefficient of acoustical materials used as wall or ceiling treatments, or the
equivalent sound absorption area of objects, such as furniture, persons or
space absorbers, in a reverberation room.
Sound absorbing materials and structures
Results of sound absorption coefficient of acoustical
materials obtained in a reverberation room.
Sound absorbing materials and structures
ISO 10534-2:1998. Acoustics — Determination of sound
absorption coefficient and impedance in impedance tubes
(or Kundt tubes)
2 microphones
loudspeaker
Sound absorbing materials and structures
What is the acoustic impedance of a material/surface?
Sound absorbing materials and structures
What is the acoustic impedance of a material/surface?
Z0 = ρ0c0 represents the
characteristic impedance of
the fluid
Sound absorbing materials and structures
Depending on the different
acoustic behaviour at
different frequencies,
sound-absorbing
materials are generally
classified into:
a) porous materials,
b) acoustic resonators
c) vibrating panels,
d) mixed systems.
Sound absorbing materials and structures
POROSITY:
viscous friction
F
CAVITY AND MEMBRANE RESONANCE:
damping of the oscillation
M
K
Sound absorbing materials and structures
POROUS MATERIALS
 open pore structure, including on the outer surface, and communicating
with each other
yes
no
 pore size << λ
complex geometric shapes that are difficult to describe with deterministic
mathematical models
with respect to sound propagation, the material seem as a homogeneous
medium, in which viscous losses occur.
 are represented by average properties of: fibre diameter, porosity, structure
factor, flow resistivity
Sound absorbing materials and structures
POROUS MATERIALS
 Fibre diameter: statistical distribution and mean value as a function of
considered density
 Porosity:
e = Vpore / Vtot
good sound absorption if e>90-95%.
Structure factor: influence of the geometric form of the material structure on
the propagation of the sound wave. It is determined by specific acoustic
measurements and it depends an the impedence values.
Sound absorbing materials and structures
POROUS MATERIALS
R=
∆p
Qv
[Pa ⋅ s/m 3 ]
Flow resistence
∆p
[Pa ⋅ s/m]
v
Specific flow resistence
Rs = R ⋅ A =
Low flow resistivity
High flow resistivity
r=
RS
∆p
=
d
v⋅d
[Pa ⋅ s/m 2 ]
Flow resistivity
(not dependent by the thickness)
If the flow resistance is high, the sound waves cannot penetrate the material; if it is
low, they do not encounter sufficient friction to dissipate the energy.
Sound absorbing materials and structures
POROUS MATERIALS
Flow resistivity (EN 29053)
Sound absorbing materials and structures
POROUS MATERIALS
Flow resistivity and Sound absorption
Sound absorbing materials and structures
POROUS MATERIALS
analytical models for calculating the sound
absorption properties of fibrous and porous
materials
• rock fibres
• glass fibres
• animal wools
• vegetable fibers or wools
• polyester fibres
• open-cell polyurethane
• foammelamine resins
• felts
• Etc
Sound absorbing materials and structures
POROUS MATERIALS
Case a) Material placed on the wall
>f>α
> thick.  > αlow freq.
Sound absorbing materials and structures
POROUS MATERIALS
Case b) Material spaced from the wall
 near wall:
Vair=0
• no friction
• minimum absorption efficiency
 far from wall:
Vair increase
absorption efficiency increases
Sound absorbing materials and structures
POROUS MATERIALS
Case b) Material spaced from the wall
Vair,max and αmax when d=λ/4
The choice of porous
material depends on:
 type of application;
 absorption;
 ease of processing;
 fire behaviour.
Sound absorbing materials and structures
POROUS MATERIALS
Absorption coefficient measured in reverberation chamber of a glass fibre panel
mounted at different distances from the wall
Sound absorbing materials and structures
POROUS MATERIALS
REVERBERATION TIME
No treatment
With porous sound absorbing treatment
Helmotz Resonator
c
f0 = 0
2π
r2
π 

V l + 

2r 
[Hz ]