Lecture 26
Goals:
• Chapters 18, entropy and second law of thermodynamics
• Chapter 19, heat engines and refrigerators
• Reading assignment for Wednesday: Chapter 20.
Physics 207: Lecture 27, Pg 1
Entropy
 A perfume bottle breaks in the corner of a room. After some time,
what would you expect?
A)
B)
Physics 207: Lecture 27, Pg 2
very unlikely
 The probability for each particle to be on the left half is ½.
probability=(1/2)N
Physics 207: Lecture 27, Pg 3
Second Law of thermodynamics
 The entropy of an isolated system never decreases. It can only
increase, or in equilibrium, remain constant.
 The laws of probability dictate that a system will evolve towards the
most probable and most random macroscopic state
 Thermal energy is spontaneously transferred from a hotter system to
a colder system.
Physics 207: Lecture 27, Pg 4
Reversible vs Irreversible
 The following conditions should be met to make a
process perfectly reversible:
1. Any mechanical interactions taking place in the
process should be frictionless.
2. Any thermal interactions taking place in the process
should occur across infinitesimal temperature or
pressure gradients (i.e. the system should always be
close to equilibrium.)
Physics 207: Lecture 27, Pg 5
Reversible vs Irreversible
 Based on the above comments, which of the following
processes is not reversible?
A. Lowering a frictionless piston in a cylinder by
placing a bag of sand on top of the piston.
B. Lifting the piston described in the previous
statement by removing one tiny grain of sand at a time.
Physics 207: Lecture 27, Pg 6
Heat Engines
Pressure
 Turning heat into work: Industrial revolution.
f
i
Volume
Physics 207: Lecture 27, Pg 7
Key concepts
 Work done by the system:
Wsystem=-Wexternal
 Energy reservoir: An object that interacts with the system, that is
sufficiently large such that its temperature is almost constant.
QH: The amount of heat transferred to/from hot reservoir
QC: The amount of heat transferred to/from cold reservoir
Physics 207: Lecture 27, Pg 8
Energy-transfer diagram
Hot reservoir
QH
cyclic system
ΔEsystem=0
QC
Wout
Wout=QH-QC
Cold reservoir
Physics 207: Lecture 27, Pg 9
Thermal efficiency
For practical reasons, we would like an engine to do the maximum
amount of work with the minimum amount of fuel. We can
measure the performance of a heat engine in terms of its thermal
efficiency η (lowercase Greek eta), defined as
We can also write the thermal efficiency as
Physics 207: Lecture 27, Pg 10

What is the largest thermal
efficiency that a heat engine
can have?
A)  =2

B)  =1
C)  =1/2
D)  =0
What is the lowest thermal efficiency that a heat
engine can have?
A)  =1/2
B)  =0
C)  =-1/2
D)  =-1
Physics 207: Lecture 27, Pg 11
Refrigerators
 Devices that uses work to transfer heat from a colder object to a
hotter object.
Hot reservoir
Win+QC=QH
QH
Win
QC
K=QC/Win
Cold reservoir
Physics 207: Lecture 27, Pg 12
Is perfect engine possible?
Hot reservoir
QH1
Wout
QH2
QH
=
Win
QC
QC
Cold reservoir
Physics 207: Lecture 27, Pg 13
Turbines: Brayton Cycle
Physics 207: Lecture 27, Pg 14
The best thermal engine ever, the Carnot engine
 A perfectly reversible engine (a Carnot engine) can be
operated either as a heat engine or a refrigerator between the
same two energy reservoirs, by reversing the cycle and with no
other changes.
 A Carnot cycle for a gas engine
consists of two isothermal processes
and two adiabatic processes
 A Carnot engine has max. thermal
efficiency, compared with any other
engine operating between TH and TC
Carnot  1 
TCold
THot
 A Carnot refrigerator has a
maximum coefficient of performance,
compared with any other refrigerator
operating between TH and TC.
K Carnot 
TCold
THot TCold
Physics 207: Lecture 27, Pg 15
The Carnot Engine

Carnot showed that the
thermal efficiency of a
Carnot engine is:
Carnot cycle
Tcold
 1
Thot
 All real engines are less efficient than the Carnot
engine because they operate irreversibly due to the
path and friction as they complete a cycle in a brief
time period.
Physics 207: Lecture 27, Pg 16