Introduction to the Second Law of Thermodynamics
(on board)
Heat engine
Thermal
efficiency

Net work output
QH
A cyclic heat engine
Examples of heat engines
: a simple steam power plant
Refrigerators and heat pumps
Coefficient
of performance
COP 
Refrigerator is a device, which
operating in a cycle, maintains a
body at a temperature lower than
the temperarature of its
surroundings.
Desired effect
Required input
Heat pump is a device, which
operating in a cycle, maintains a
body at a temperature higher than
the surroundings.
Example of a refrigerator
• A vapor compression refrigeration system
Introduction to the Second Law of Thermodynamics
Introducing the second law
• A process should satisfy the first law in order
to occur.
• However, satisfying first law alone does not
guarantee that the process will take place.
Examples of impossible processes that do
not violate first law
• One more:
A cup of coffee does not get hotter
in a cooler room by absorbing
heat from environment.
Transferring heat to a resistance will not generate
electrical energy
Heat
Transferring heat to this paddle-wheel device
will not cause the paddle-wheel to rotate and
raise the mass through the pulley.
Work was completely converted into heat
in Joule’s experiment
Q=W
Some definitions (on board/discussion)
• Thermal energy reservoirs (source and sink)
• Heat engines
• Efficiency of a heat engine
Example of an heat engine: a
simple steam power plant
Introducing the second law
• A process should satisfy the first law in order
to occur.
• However, satisfying first law alone does not
guarantee that the process will take place.
Examples of impossible processes that do
not violate first law
• One more:
A cup of coffee does not get hotter
in a cooler room by absorbing
heat from environment.
Transferring heat to a resistance will not generate
electrical energy
Heat
Transferring heat to this paddle-wheel device
will not cause the paddle-wheel to rotate and
raise the mass through the pulley.
Statements of the second law
• Two equivalent ways the second law can be stated are due to:
– Kelvin and Planck (“The Kelvin-Planck statement”)
– Clausius (“The Clausius statement”).
• The direction in which processes actually occur can be judged
by taking the help of these two statements.
• Either of this statements can be used to detect impossible
inventions and impossible processes.
Outline of our course of progression on
second law
1. DEDUCTION BASED ON either of the Kelvin-Planck and
Clausius statements will give us the ability to
C) state second law as an inequality involving engines/refrigerators in
contact with more than one reservoirs
B) Assign temperature values from a non-empirical perspective and
find the most efficient refrigerators/engines
2. Following step 1, the property entropy will be defined to
allow another more mathematical statement of the second
law and another way to judge the actual direction of
processes.
The Kelvin Planck Statement of the Second
Law
• It is impossible for any device that operates in
a cycle to receive heat from a single reservoir
and produce a net amount of work.
• Equivalently:
– “no heat engine can have a thermal efficiency of
100%”.
– “For a power plant to operate, the working fluid
must exchange heat with the environment as well
as the furnace.”
A heat engine that violates the Kelvin
Planck statement
You need more than one reservoir to convert
heat to work by a cyclic engine (a cold
reservoir, is needed to dump the heat which
could not be converted to work).
Stating the Kelvin Planck statement
analytically
• The Kelvin-Planck statement do not forbid cyclic
devices operating with a single reservoir, but insists
that such a cyclic device should receive work.
• So, according to the Kelvin Planck statement
W1TER,cycle,net  0
Clausius statement of the second law of
thermodynamics
• It is impossible to construct a device that
operates in a cycle and produces no effect
other than the transfer of heat from a lower
temperature body to a higher temperature
body.
• A refrigerator is not a self-acting device:
energy (electrical work to the motor driving
the compressor) has to be provided from the
surroundings to run a refrigerator.
A refrigerator that violates the Clausius
statement
Equivalence of Kelvin-Planck and Clausius
statements
• Violation of Clausius statementViolation of
Kelvin-Planck statement
• Violation of Kelvin-Planck statementViolation of
Clausius statement
Violation of KP  Violation of Clausius
TH
TH
Q1
Q
HE!
Q2
=Q1+W
=Q1+Q
W
HE!+R
R
Q1
Q1
TC
TC
The net heat exchange of the cyclic
device (HE+R) with the hot reservoir=Q2-Q
Violation of Clausius  Violation of KP
TH
Q
Q
W
HE+R!+TH
W
HE
R!
Q-Q1
Q
Q1
TC
TC
KP statement requires the device in contact with the single reservoir (here at Tc)
to be a cyclic device. Because nothing happens to the TH reservoir (Qin=Qout=Q).
the combined device (HE+R!+TH) is a cyclic device.
Violation of Clausius  Violation of KP
(Alternative)
TH
Q
Q
Q
W
W
HE
HE+R!
R!
Q-Q1
Q
Q1
TC
TC
TH can be eliminated and Q can be fed directly to H from R
Equivalence of Kelvin-Planck and Clausius
statements
• Violation of Clausius statementViolation of
Kelvin-Planck statement
• Violation of Kelvin-Planck statementViolation of
Clausius statement
Perpetual motion machines (PMM)
• Any device that violates the first or the second law of
thermodynamics is called a perpetual motion
machine.
• Violates the First law: “perpetual machine of the first
kind”: produces more energy than supplied.
• Violates the Second law: “perpetual motion machine
of the second kind”: Allows the efficiency of cyclic
heat engines to equal 100%.
Example of a PMM1
OK
Wnet ,out  Wout Win
Not OK! Produces net
energy output (Qout  Wout )
without energy input.
Identifying PMM2 by KelvinPlanck/Clausius statement
• A PMM2 according to Kelvin-Planck statement is a device that:
 Operates in a cycle.
 Accepts heat from a single reservoir (surroundings).
 Develops a net work output.
• Example: A power plant with no condenser
OK
Not
OK!
Violates
KP
Identifying PMM2 by Clausius
statement
• A PMM2 according to Clausius statement is a device whose
operation has the sole effect of transfer of
heat from a low termperature to high temperature body.
tH
tC
How to make the most efficient heat
engine
• Second law: no heat engine can have an
efficiency of 100%.
• So, what is the maximum efficiency?
• It turns out (shown later) that maximum
efficiency is realized when a heat engine runs
on a cycle consisting of certain “idealized
processes”.
Reversible process
vacuum
• Reversible processes can be reversed
leaving no trace on the surroundings.
• If the original process and its reverse is combined into a cycle, after the
cycle is executed,
– both the system and surroundings will return to their original state.
– If the surroundings can be considered as a single thermal energy reservoir, no net
heat and work exchange between the system and surroundings occurs during this
cycle.
• Examples:
– Pendulum swinging in vacuum (can be studied in mechanical coorddinates alone)
– Reversible work (slow or “quasiequilibrium expansion”)
– Reversible heat transfer (on board)
– Combinations thereof
Irreversible processes
•
•
•
Processes that are not reversible are
irreversible.
After an irreversible process is executed, it
is impossible to restore both the system
and the surroundings to the original state.
All “natural” or “spontaneous” processes are
irreversible.
Irreversibilities
• Factors that render a process irreversible are
irreversibilities.
• Examples:
–
–
–
–
–
–
–
Friction
Unrestrained expansion, fast expansion/contraction
Heat transfer through a finite temperature difference
Electric current flow through a resistance
Inelastic deformation
Mixing of matter with different compositions/states
chemical reaction
Characteristics of reversible and irreversible processes
Reversible process
Irreversible process
• In the intermediate stages
• Passes through a succession of
the system is not in
thermodynamic equilibrium states.
thermodynamic equilibrium.
• Infinitely slow.
• Fast.
• Driving forces (DT, DP etc.) between
the system and the surroundings and
• Driving forces (DT, DP etc. )
within parts of the system are
between the system and
infinitesimal in magnitude.
the surroundings and within
• Dissipative mechanisms (work done
parts of the system have
on the system incompletely converting
finite magnitude.
to KE/PE change of the system) such as
friction, Joule heating, inelastic
• Dissipative mechanisms
deformation should be absent.
are present.
To show that heat transfer through a finite temperature
difference is an irreversible process
tH
tH
Q1-Q
Q1
W=Q1-Q
H
Q
W=Q1-Q
Q
tC
Violation of Kelvin Planck
statement
Note: Heat transfer through an infinitesimal temperature difference is a reversible
process.
Irreversible processes
•
•
•
Processes that are not reversible are
irreversible.
After an irreversible process is executed, it
is impossible to restore both the system
and the surroundings to the original state.
All “natural” or “spontaneous” processes are
irreversible.
Irreversibilities
• Factors that render a process irreversible are
irreversibilities.
• Examples:
–
–
–
–
–
–
–
Friction
Unrestrained expansion, fast expansion/contraction
Heat transfer through a finite temperature difference
Electric current flow through a resistance
Inelastic deformation
Mixing of matter with different compositions/states
chemical reaction
Irreversibilities
• Factors that render a process irreversible are
irreversibilities.
• Examples:
–
–
–
–
–
–
–
Friction
Unrestrained expansion, fast expansion/contraction
Heat transfer through a finite temperature difference
Electric current flow through a resistance
Inelastic deformation
Mixing of matter with different compositions/states
chemical reaction
How to conduct a reversible process?
• To conduct a process reversibly, at every stage of the there
should be negligible “driving forces” from “property
differentials between system and surroundings” such as DT,
DP, D(composition), so that the system is “not driven” out of
thermodynamic equilibrium.
• Reversible processes are therefore very slow.
• Example:
• Reversible heat transfer (on board)
• Reversible expansion/contraction (discussed with respect
to quasi-equilibrium process)
The system stays infinitesimally close to thermodynamic equilibrium during a reversible
process. In practice, a thermodynamic process can at most approach reversibility With
DT0, DP0 etc.
Reversible expansion/compression
W=nw
One small weight is removed at a time and the gas expands from a
a volume Vi to a volume Vf (see also discussion on quasiequilibrium process).
patm
p, V
Usefulness of reversible processes: a demonstration
W=nw
patm
pi , Vi
p
Find work done by the system on surroundings when:
Process 1: One small weight is removed at a time and the gas
expands from a volume Vi to a volume Vf.
Process 2: All of the weights are removed at once from the
piston at t=0 (an irreversible process) expands from a volume Vi to
a volume Vf
Here, in order to keep the end states same; both processes are
carried out isothermally.
Note the careful choice of system boundary.
In this diagram,
p=patm is not the
Initial state: (pi=patm+W/A,Vi)
pressure of the system.
Final state: (pf=patm,Vf)
p=patm
p=patm
p
V
wrev / irrev   Fboundary dx   Pboundary dV
wirrev  patm (Vi  V f )  wrev
V
Internal and external irreversibilities
• Internal irreversibility:
Irreversibility located within the system boundaries.
• External irreversibility:
Irreversibility located outside the system boundary; usually in the part of surroundings
immediately adjacent to the system boundary.
• Internally reversible process:
An idealization of a process in which no internal irreversibilities are present.
• (Totally) reversible process:
A process with no internal and external irreversibilities.
Another example:
Example: thermal energy reservoirs
undergo internally reversible processes
(add to definition)
Interpretation depends on choice of
system boundary.
Internally reversible process
proceed through a succession of
equilibrium states
=quasi-equilibrium process
Reversible and irreversible processes between
two equilibrium states
p
v
The path of an irreversible process cannot be shown on
a property diagram, since intermediate states are not
equilibrium states. The dotted line (shape does not matter) is
just a convention to represent irreversible processes.
To show that a process is irreversible
A process can be shown to be irreversible if it
does not conform to the definition of a
reversible process
Non-zero energy exchange with the surroundings is required to
return the system to initial state.
Example of irreversibility due to lack of equilibrium:
unrestrained expansion of a gas
A
800 kPa
B
0 kPa
A membrane separates a gas in chamber A from vacuum
in chamber B. The membrane is ruptured and the gas expands
Into chamber B until pressure equilibrium is established. The
process is so fast and the container is insulated enough such
that negligible heat transfer takes place between
the gas and the surroundings during this process.
At the end of the unrestrained expansion process, the gas (system) has
the same internal energy, as it had initially.
To show that unrestrained expansion is an irreversible
process
800 kPa
0 kPa
400 kPa
System (gas) has
been restored.
Qout
800 kPa
0 kPa
Converting Qout back completely to
work by a cyclic device
is impossible according to
second law; hence the surroundings
cannot be restored.
Vacuum pump
Win