CHAPTER 3
ENERGY TRANSFER BY
HEAT, WORK AND MASS
1 kg iron
1 kg water
Which
Whichtakes
takesmore
moreenergy
energy? ?
Which takes more energy ?
oC to 30oC
To
raise
the
temperature
of
1
kg
iron
from
20
To raise the temperature of 1 kg iron from 20oC to 30oC
oC
Tooror
raise the temperature of 1 kg iron from 20oC to
30
oC to 30oC ?
To
raise
the
temperature
of
1
kg
water
from
20
or
To raise the temperature of 1 kg water from 20oC to 30oC ?
To raise the temperature of 1 kg water from 20oC to 30oC ?
SPECIFIC HEATS
• It takes different amounts of energy to raise the temperature
of identical masses of different substances by one degree
• We need about 4.5 kJ of energy to raise the temperature of
1 kg of iron to from 20 to 30oC
• It takes about 41.8 kJ of energy to raise the temperature of 1
kg liquid water from 20 to 30oC
SPECIFIC HEATS
•
It is desirable to have a property that will enable us to
compare the energy storage capabilities of various substances
•
This property is the specific heat
• The specific heat is defined as the energy required to raise the
temperature of a unit mass of a substance by one degree
SPECIFIC HEATS
• In thermodynamics, we are interested in
two kinds of specific heats:
Specific heat at constant volume, Cv
Specific heat at constant pressure, Cp
 u 

• Cv is defined as : Cv = 
 T v
 h 

• Cp is defined as : C p = 
 T  p
SPECIFIC HEATS
• These equations are property relations and are
independent of the type of processes
• They are valid for any substance undergoing any process
• Like any other property, the specific heats
depend on the state of a substance
SPECIFIC HEATS
• Cv is related to the changes in internal energy
• It is a measure of the variation of internal energy of a
substance with temperature
•
Cp is related to the changes in enthalpy
• It is a measure of the variation of enthalpy of a substance with
temperature
•
•
A common unit for specific heats is kJ/kg.oC or kJ/kg.K
SPECIFIC HEATS OF IDEAL GASES
•
The behaviour of an ideal gas is given by the relationship
Pv = RT
• It has been demonstrated mathematically & experimentally
that for an ideal gas, the internal energy is a function of
temperature only, i.e :
u = f (T)
SPECIFIC HEATS OF IDEAL GASES
• Using the definition of enthalpy and the
equation of state of an ideal gas :
❖ Pv = RT
❖ h =u + Pv
❖ h = u + RT
• Since R is constant and u = f (T), it follows
that the enthalpy of an ideal gas is a also a
function of temperature only:
h = f (T)
SPECIFIC HEATS OF IDEAL GASES
• Since u and h depend only on temperature
for an ideal gas, the specific heats Cv and
Cp also depend on temperature only
• Thus, the partial derivatives in the
definition for Cv and Cp can be replaced by
ordinary derivatives
 u 
Cv =  
 T v
 h 
Cp =  
 T  p
INTERNAL ENERGY & ENTHALPY OF IDEAL GASES
• The differential changes in the internal energy and
enthalpy of an ideal gas is given by:
❖ du = Cv (T) dT
❖ dh = Cp (T) dT
• The change in internal energy or enthalpy for an ideal
gas during a process from state 1 to state 2 is obtained
by integrating the above equations
INTERNAL ENERGY & ENTHALPY OF IDEAL GASES
• There are 3 ways to determine the internal energy and
enthalpy changes of ideal gases :
• First method:
o By using the tabulated u and h data ( Table A-17)
o This is the easiest and most accurate
INTERNAL ENERGY & ENTHALPY OF IDEAL GASES
• Second method:
o By using the Cv and Cp relations as a function
of temperature and performing the integrations
(Table A-2c). This is inconvenient for hand
calculations but desirable for computerized
calculations
INTERNAL ENERGY & ENTHALPY OF IDEAL GASES
• Third method:
By using average specific heats (Table A-2b)
• This is very simple and convenient when property tables
are not available
• They are reasonably accurate if the temperature interval
is not very large
INTERNAL ENERGY & ENTHALPY OF IDEAL GASES
• The Du and Dh of ideal gases are expressed as
2
Du = u2 − u1 =  Cv (T )dT  Cv ,av (T2 − T1 )
1
2
Dh = h2 − h1 =  C p (T )dT  C p , av (T2 − T1 )
1
• Cv,av and Cp,av are evaluated from Table A-2b at the
average temperature (T1 + T2)/2
If T1 = 300 K and T2 = 400 K
Tavg = 350 K
If T1 = 300 K and T2 = 400 K
Tavg = 350 K
Du = 0.721 x (400 - 300)
= 72. 1 kJ/kg
In our class, we will you use the
third method where Cv,avg & Cp,avg
values will be provided.
ADDITIONAL RELATIONSHIPS FOR IDEAL GASES
• A special relationship between Cv and Cp
for ideal gases can be obtained by
differentiating the relation h = u + RT, which yields:
dh = du + RdT
• Replacing dh by CpdT and du by CvdT and
dividing the results by dT, we obtain
Cp = Cv + R
ADDITIONAL RELATIONSHIPS FOR IDEAL GASES
Cp = Cv + R
• This is an important relationship since it
enables us to determine Cv from a knowledge of Cp and
the gas constant R
• The specific heat ratio k is defined as
k = Cp/Cv
Attendance Sec 01:
https://forms.gle/7t9KER2CKYQrqdVv9
Attendance Sec 02:
https://forms.gle/9PRWEhcWUanNPjdr6
Heat
• Heat is defined as the form of energy that is transferred
between 2 systems ( or a system and its surroundings)
by virtue of a temperature difference
• An energy interaction is heat only if it takes place
because of a temperature difference
• There cannot be any heat transfer between 2
systems that are at the same temperature
Heat
• In thermodynamics, the term heat simply means heat transfer
• A process during which there is no heat transfer is
called an adiabatic process
• There are 2 ways in which a process can be
adiabatic:
The system is well insulated so that only a negligible
amount of heat can pass through the boundary
Both the system and the surroundings are at the same
temperature and therefore there is no driving force
(temperature difference) for heat transfer
Heat
• An adiabatic process should not be confused with
an isothermal process
• Even though there is no heat transfer during an
adiabatic process, the energy content and thus
the temperature of a system can still be changed
by other means such as work
• The unit for heat is kJ
Heat
• The amount of heat transferred during the process
between 2 states ( states 1 and 2 ) is denoted by 1 Q2
• Heat transfer per unit mass of a system is
denoted by q,
q = Q/m
(kJ/kg)
• The unit for heat is kJ
Heat
•
• The rate of heat transfer is denoted by Q , where
the overdot stands for the time derivative, or per
unit time
• The heat transfer rate has the unit kJ/s, which is
equivalent to kW
Heat
•
• When Q varies with time, the amount of heat •transfer
during a process is determined by integrating Q
over the time interval of the process:
2
Q=
•
 Qdt
1
Heat
•
• When Q remains constant during a process, the
relation reduces to :
•
Q = Q Dt
(kJ)
Dt = t2 – t1 is the time interval during which
the process occurs
Heat
• Heat is transferred by 3 mechanisms:
• Conduction is the transfer of energy from the
more energetic particles of a substance to the
adjacent less energetic ones as a result of
interaction between particles
• Convection is the transfer of energy between a
solid surface and the adjacent fluid that is in
motion, and it involves the combined effects of
conduction and fluid motion
• Radiation is the transfer of energy due to the
emission of electromagnetic waves