Thermodynamics II
The First Law of Thermodynamics
•
Heat and Work. First Law of Thermodynamics
•
Heat and Work on Quasi-Static Processes for a Gas.
The Second Law of Thermodynamics
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Heat Engines and the Second Law of Thermodynamics
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Refrigerators and the Second Law of Thermodynamics
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The Carnot Engine
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Heat Pumps
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Irreversibility and disorder. Entropy
References: Tipler; wikipedia,…
The First Law of Thermodynamics
Energy exists in many forms, such as mechanical energy, heat,
light, chemical energy, and electrical energy. Energy is the
ability to bring about change or to do work.
Thermodynamics is the study of energy.
Surroundings
System
The boundary of the system
is arbitrarily chosen
The system can exchange mass and energy
through the boundary with the environment.
An example of “closed system” - no mass flow- is
the gas confined in a cylinder. The boundary –in
this case real wall- is made by the cylinder and the
piston walls.
The First Law of Thermodynamics
First Law of Thermodynamics → Conservation of Energy:
Energy can be changed from one form to another, but it cannot be created or
destroyed. The total amount of energy and matter in the Universe remains
constant, merely changing from one form to another.
The First Law of Thermodynamics (Conservation) states that energy is
always conserved, it cannot be created or destroyed. In essence,
energy can be converted from one form into another.
The energy balance of a system –as a consequence of FLT- is a
powerful tool to analyze the exchanges of energy between the system
and its environment.
We need to define the concept of internal energy of the system, Eint as
an energy stored in the system.
Warning: It is not correct to say that a system has a large amount of
heat or a great amount of work
http://www.emc.maricopa.edu/faculty/farabee/BIOBK/BioBookEner1.html
The First Law of Thermodynamics. Heat, Work and Internal Energy
Joule’s Experiment and the First Law of Thermodynamics.
Equivalence between work and heat
1 calorie = 4.184 Joules
Work is done on water. The energy is transferred to
the water – i. e. the system- . The energy transferred
appears as an increase in temperature.
We can replace the insulating walls by conducting
walls. We can transfer heat through the walls to the
system to produce the same increase in temperature.
Schematic diagram for Joule´s
experiment. Insulating walls are
necessary to prevent heat transfer
from the enclosed water to the
surroundings.
As the weights fall at constant speed,
they turn a paddle wheel, which does
work on water.
If friction in mechanism is negligible,
the work done by the paddle wheel on
the water equals the change of
potential energy of the weights.
The increase in temperature of the system is a
consequence of an increase in Internal Energy.
Internal energy is a state function of the system
The sum of the heat transferred into
the system and the work done on the
system equals the change in the
internal energy of the system
Eint  Qin  Won
The First Law of Thermodynamics
Another method of
doing work.
Electrical work is
done on the
system by the
generator, which
is driven by the
falling weight.
The First Law of Thermodynamics. Application to a particular case:
A gas confined in a cylinder with a movable piston
The state of the gas will be
described by the Ideal Gas Law.
PV  n R T
How does the confined gas
exchange energy (heat and
work) with the surroundings?.
What is the value of the internal
energy for the gas in the cylinder?
First Law
Eint  Qin  Won
dEint  Qin  Won
How can we calculate the
energy –heat and/or worktransferred, added or
subtracted, to the system?
“Quasi static processes”: a type of process where the gas moves through a
series of equilibrium states. Then, we can apply the Ideal Gas Law. In practice, if
we move the piston slowly, it will be possible to approximate quasi-static processes
fairly well.
First Law of Thermodynamics. Fluxes of energy and mass on the earth
surface. Energy balance.
Rn = Rns + Rnl
λET
ΔE
H
Ph
Ph
CO2
Energy fluxes:
Rn : Net gain of heat energy from
radiation
λET Latent heat, Energy associated
to the flux of water vapor leaving
from the system
H Sensible Heat.
G Heat energy by conduction to the
D
soil
Ph: Net photosynthesis
ΔEint: Change of the internal energy
of the system
D: Advection
G
Net fluxes of mass
Water vapor
Carbon –CO2
Energy balance (applying First Law):
Rn – H – λET – G – D - Ph = ΔEint
The First Law of Thermodynamics. Application to a particular case:
A gas confined in a cylinder with a movable piston
Internal Energy for an Ideal Gas.
It only depends on the temperature of
the gas, and not on its volume nor its
pressure
Experiment: Free expansion.
For a gas at low density – an ideal gas-, a
free expansion does not change the
temperature of the gas.
What is the value of the internal
energy for the gas in the cylinder?
If heat is added at constant volume, no work
is done, so the heat added equals to the
increase in thermal energy
Eint  Qin
Qin  CV T
and
dEint  CV dT  n cV dT
Internal Energy is a state function, i.e. it is not dependent on the
process, it only depends of the initial and final temperature
The First Law of Thermodynamics. Application to a particular case:
A gas confined in a cylinder with a movable piston
Heat transferred to a system
If heat is added at constant
pressure the heat energy
transferred will be used to
expand the substance and to
increase the internal energy.
QP  CP T
QP  CP dT
If the substance expands, it
does work on its surroundings.
Applying the First Law of Thermodynamics
If heat is added at constant
volume, no work is done, so
the heat added equals the
increase in thermal energy
Qin,V  CV dT  n cV dT
Qin,V  CV T  n cV T
dEint  QP  Won  CP dT  PdV
PdV  (CP  CV ) dT
as d ( PV )  PdV  dP V
and P  const  dP  0
CP  CV  n R
The expansion is usually negligible for solids
and liquids, so for them CP ~ CV.
The First Law of Thermodynamics. Application to a particular case:
A gas confined in a cylinder with a movable piston
Heat transferred to a system. A summary
Heat energy can be added to (or lost from) the system. The value of the heat
energy transferred depends on the process.
Typical processes are
QV  CV T ; QV  CV dT
- At constant volume
- At constant pressure
Ideal Gas
For the case of ideal gas
QP  CP T ; QP  CP dT
CP  CV  n R Relationship of Mayer
From the Kinetic theory,
for monoatomic gases
for biatomic gases
3
CV  n R
2
5
CV  n R
2
For solids and liquids, as the expansion at constant pressure is usually
negligible CP ~ CV.
Adiabatic: A process in which no heat flows into or out of a system is
called an adiabatic process. Such a process can occur when the system is
extremely well insulated or when the process happens very quickly.
The First Law of Thermodynamics. Application to a particular case:
A gas confined in a cylinder with a movable piston
Work done on the system, Won , is the energy transferred as work to the system.
When this energy is added to the system its value will be positive.
The work done on the gas in an
expansion is
V2
Won gas    P dV
V1
Won gas  Wby gas
P- V diagrams
Constant pressure
V2
Won gas    P dV  P(V1  V2 )
V1
If 5 L of an ideal gas at a pressure of 2 atm is cooled
so that it contracts at constant pressure until its
volume is 3 L what is the work done on the gas?
[405.2 J]
The First Law of Thermodynamics. P-V diagrams
P- V diagrams
Conecting an initial state and a final state
by three paths
Isothermal
V2
Constant pressure
Constant Volume
Constant Temperature
Won gas    P dV  P(V1  V2 )
V1
V2
Won gas    P dV  0
V1
V2
Won gas   
V1
n RT
V2
dV  n R T ln
V
V1
The First Law of Thermodynamics
A biatomic ideal gas undergoes a cycle starting at
point A (2 atm, 1L). Process from A to B is an
expansion at constant pressure until the volume is 2.5
L, after which, it is cooled at constant volume until its
pressure is 1 atm. It is then compressed at constant
pressure until the volume is again 1L, after which it is
heated at constant volume until it is back to its original
state. Find (a) the work, heat and change of internal
energy in each process (b) the total work done on the
gas and the total heat added to it during the cycle.
A system consisting of 0.32 mol of a monoatomic ideal gas
occupies a volume of 2.2 L, at a pressure of 2.4 atm.
The system is carried through a cycle consisting:
1. The gas is heated at constant pressure until its volume
is 4.4L.
2. The gas is cooled at constant volume until the pressure
decreases to 1.2 atm
3. The gas undergoes an isothermal compression back to
its initial point.
(a) What is the temperature at points A, B and C
(b) Find W, Q and ΔEint for each process and for the entire
cycle
The First Law of Thermodynamics. Processes. P-V Diagrams
Adiabatic Processes. No heat flows into or out of the system
The First Law of Thermodynamics. Processes. P-V Diagrams
Adiabatic Processes. No heat flows into or out of the system
Qin  0
Adiabatic process
then Eint  Won,adiabatic  n cV T
The equation of curve describing the adiabatic
process is
P V   const ;  
T V  1  const
T  P1  const
A quantity of air is compressed adiabatically
and quasi-statically from an initial pressure of
1 atm and a volume of 4 L at temperature of
20ºC to half its original volume. Find (a) the
final pressure, (b) the final temperature and (c)
the work done on the gas.
cP = 29.19 J/(mol•K); cV = 20.85 J/(mol•K).
M=28.84 g
CP
CV
adiabatic coefficient
We can use the ideal gas to rewrite
the work done on the gas in an
adiabatic process in the form
Won gas,adiab 
Pf V f  Pi Vi
 1
The First Law of Thermodynamics.
Cyclic Processes. P-V Diagrams
Two moles of an ideal monoatomic gas have an initial pressure P1 = 2 atm and an initial
volume V1 = 2 L. The gas is taken through the following quasi-static cycle:
A.- It is expanded isothermally until it has a volume V2 = 4 L.
B.- It is then heated at constant volume until it has a pressure P3= 2 atm
C.- It is then cooled at constant pressure until it is back to its initial state.
(a) Show this cycle on a PV diagram. (b) Calculate the heat added and the work done by
the gas during each part of the cycle. (c) Find the temperatures T1, T2, T3
The First Law of Thermodynamics.
Cyclic Processes. P-V Diagrams
The First Law of Thermodynamics.
Cyclic Processes. P-V Diagrams
At point D in the figure the pressure and
temperature of 2 mol of an ideal monoatomic gas
are 2 atm and 360 K. The volume of the gas at point
B on the PV diagram is three times that at point D
and its pressure is twice that at point C. Paths AB
and DC represent isothermal processes. The gas is
carried through a complete cycle along the path
DABCD. Determine the total work done by the gas
and the heat supplied to the gas along each portion
of the cycle
The First Law of Thermodynamics.
Cyclic Processes. P-V Diagrams
The First Law of Thermodynamics.
Cyclic Processes. P-V Diagrams