Topic 10: Thermal physics
10.3 The second law and entropy
10.3.1 State that the second law of
thermodynamics implies that thermal energy
cannot spontaneously transfer from a region
of low temperature to a region of high
temperature.
10.3.2 State that entropy is a system property
that expresses the degree of disorder of a
system.
10.3.3 State the second law of thermodynamics in
terms of entropy changes.
10.3.4 Discuss examples of natural processes in
terms of entropy changes.
Topic 10: Thermal physics
10.3 The second law and entropy
State that the second law of thermodynamics
implies that thermal energy cannot spontaneously
transfer from a region of low temperature to a
region of high temperature.
In the previous lesson we studied
hot reservoir
at TH
the heat engine.
Because heat energy has a tendency
QH
to flow from objects of high
temperature to objects of low
engine W
temperature, useful work can be
harvested during the process.
Visualize the internal combustion
QL
engine where fuel and oxygen
ignite to produce great heat, which cold reservoir
at TL
then does work, and is exhausted at
a lower temperature.
Topic 10: Thermal physics
10.3 The second law and entropy
State that the second law of thermodynamics
implies that thermal energy cannot spontaneously
transfer from a region of low temperature to a
region of high temperature.
Because heat energy does NOT have a
hot reservoir
at TH
tendency to flow from objects of LOW
temperature to objects of HIGH
QH
temperature, the reverse process does
not naturally occur.
pump
W
If we want it to happen, we must do
work ON the system.
This is what a heat pump does.
QL
Visualize the refrigerator, which
cold reservoir
through external work removes heat
at TL
from cold objects inside and pumps
it into the warm air outside.
Topic 10: Thermal physics
10.3 The second law and entropy
State that the second law of thermodynamics
implies that thermal energy cannot spontaneously
transfer from a region of low temperature to a
region of high temperature.
The second law of thermodynamics has various
forms of statement:
STATEMENT 1: (Has to do with heat pumps.)
”Heat will not flow spontaneously from a colder
body into a warmer body.”
STATEMENT 2: (Has to do with heat engines.)
”No heat engine which operates in a cycle can be
100% efficient.”
FYI
A corollary to Statement 2 is that “it is not
possible to construct a perpetual motion
machine.” Why?
Topic 10: Thermal physics
10.3 The second law and entropy
State that the second law of thermodynamics
implies that thermal energy cannot spontaneously
transfer from a region of low temperature to a
region of high temperature.
An analysis of possible cycles for heat engines
performed by the great Boffins on high has shown
that the following processes on an ideal gas
would produce the maximum efficiency per cycle:
(AB) An isothermal expansion.
The Carnot Cycle
(BC) An adiabatic expansion.
P
A
(CD) An isothermal contraction.
(DA) An adiabatic contraction.
B
FYI
We call this cycle a Carnot cycle.
D
An engine having maximum efficienC
cy is called a Carnot engine.
V
Topic 10: Thermal physics
10.3 The second law and entropy
State that the second law of thermodynamics
implies that thermal energy cannot spontaneously
transfer from a region of low temperature to a
region of high temperature.
The efficiency of a Carnot engine can be
calculated using the following relationship:
Efficiency = 1 – ( Tcold / Thot )
The temperatures are absolute.
EXAMPLE: Find the efficiency of a
Carnot engine having an operating
temperature of 1500ºC which
exhausts into 20ºC ambient air.
SOLUTION: Tcold = 293 K and Thot =
1773 K so that
Efficiency = 1 - 293/1773 = 0.85.
efficiency of a
Carnot engine
The Carnot Cycle
P
A
B
D
C
V
Topic 10: Thermal physics
10.3 The second law and entropy
State that the second law of thermodynamics
implies that thermal energy cannot spontaneously
transfer from a region of low temperature to a
region of high temperature.
It turns out that Statement 1 and Statement 2 can
be shown to be equivalent. (Not by us, mind you!)
Recall our Sankey Diagrams from Topic 8:
CHEMICAL POTENTIAL
ENERGY
ENERGY
KINETIC
ENERGY
ELECTRICAL
ENERGY
Note that every process in the diagram is
inefficient to some extent, and energy (the
yellow) is lost at each conversion.
Topic 10: Thermal physics
10.3 The second law and entropy
State that entropy is a system property that
expresses the degree of disorder of a system.
We now define the entropy S of a system to be the
degree of disorder of that system.
EXAMPLE: Consider the divided container
that has its lower half filled with a gas
under pressure. A feather rests on top of
the divider.
When we pull out the divider, the air
does work on the feather, increasing its
potential energy (at least temporarily).
We say that the system (of container,
gas and feather) has become more
disordered. Thus ∆S > 0. (S increased.)
Furthermore, the original order cannot
come back spontaneously.
Topic 10: Thermal physics
10.3 The second law and entropy
State that entropy is a system property that
expresses the degree of disorder of a system.
We now define the entropy S of a system to be the
degree of disorder of that system.
Measuring the entropy S of a system is difficult.
However, measuring its change in entropy ∆S can
be done quite easily.
When thermal energy Q is given to (or taken from)
a system having an absolute temperature T, the
system’s change in entropy ∆S is given by
∆S = Q/T
change in entropy
of a system
and is measured in J K-1. Its sign is that of Q.
FYI
If the temperature T of a system changes during
a thermodynamic process, we must use calculus.
Topic 10: Thermal physics
10.3 The second law and entropy
State that entropy is a system property that
expresses the degree of disorder of a system.
∆S = Q/T
change in entropy
of a system
PRACTICE: Find the change in entropy caused by
freezing 50 grams of water at 0°C to ice at 0°C.
SOLUTION:
Recall from Topic 3 that during phase changes T
remains constant. Thus the formula ∆S = Q/T
applies, with T a constant 273 K.
During phase change we use Q = mL.
For freezing water we remove energy so that
Q = -mL
= -(.050 kg)(3.33105 J/kg) = -16650 J.
Then ∆S = Q/T = (-16650 J) / 273 K = -60 J K-1.
Since the entropy decreased that means that the
order of the system increased. Did it?
Topic 10: Thermal physics
10.3 The second law and entropy
State the second law of thermodynamics in terms
of entropy changes.
The second law can also be expressed in terms of
entropy:
STATEMENT 3: (Has to do with entropy.)
”In any process, the entropy of the universe must
either stay the same, or it must increase.”
EXAMPLE: Our previous example showed that the
entropy of the ice cube decreased. Does this
violate the second law of thermodynamics?
SOLUTION: No, it does not.
We looked only at the change in entropy of the
ice cube and ignored the process used to freeze
the water.
As a whole, we put more heat into the system
containing the ice cube than we took out.
Topic 10: Thermal physics
10.3 The second law and entropy
State the second law of thermodynamics in terms
of entropy changes.
The freezer
hot reservoir
PRACTICE: Show the complete system
at TH
used in the process of making the
ice cube.
QH
SOLUTION: Use energy diagrams:
The power plant
pump
CHEMICAL POTENTIAL KINETIC ELECTRICAL W
ENERGY ENERGY
ENERGY
ENERGY
QL
cold reservoir
at TL
The heat energy represented in yellow is
dissipated in the environment (increasing its
entropy) and far outweighs the loss of entropy of
the water!
Topic 10: Thermal physics
10.3 The second law and entropy
Discuss examples of natural processes in terms of
entropy changes.
”In any process, the entropy of the universe must
either stay the same, or it must increase.”
∆S = Q/T
change in entropy
of a system
Note that there are two ways to increase the
entropy of a system.
(1) Increase Q, the thermal energy of the system.
(2) Decrease T, the temperature of the system.
PRACTICE: Discuss why the universe is tending
toward a temperature of 0 K (its so-called heat
death).
SOLUTION: Assuming that Q is a fixed quantity in
the universe as a whole, and that the entropy S
is ever increasing, T must eventually approach 0.
Topic 10: Thermal physics
10.3 The second law and entropy
Discuss examples of natural processes in terms of
entropy changes.
EXAMPLE: Entropy has been called “the arrow of time.”
Consider a wine glass that has been shattered.
(a) Explain how its entropy has increased.
(b) Explain how entropy prevents the glass from
spontaneously reassembling itself.
SOLUTION:
(a) The glass is certainly more
disorganized. It has lost potential
energy, for example. The wine is
dispersed.
(b) Reassembling the glass will
increase its order (decrease its
entropy). According to the second
law this can’t happen by itself.
Topic 10: Thermal physics
10.3 The second law and entropy
Discuss examples of natural processes in terms of
entropy changes.
Here are some “fun” facts about entropy.
(1) Net entropy can be increased, but never
reduced.
(2) Since all natural processes create entropy,
the evolution of the universe will continue to
increase the entropy.
(3) Thus, no matter how organized the universe
appears, its tendency to disorganization is ever
growing.
(4) At the beginning of the big bang, the
temperature of the universe was extremely high.
Hence the entropy low. S has increased ever
since.
(5) T is presently about 3 K, and dropping!
Topic 10: Thermal physics
10.3 The second law and entropy
Discuss examples of natural processes in terms of
entropy changes.
An increase in disorder of the system.
In any process the entropy of the universe
must stay the same, or increase.
During the development of the embryo, the
egg must give off enough heat so that the
surroundings have an increase in entropy
greater than the chicken’s decrease.
Topic 10: Thermal physics
10.3 The second law and entropy
Discuss examples of natural processes in terms of
entropy changes.
The refrigerator adds more heat
to the air than it removes.
Thus BOTH increase.
Topic 10: Thermal physics
10.3 The second law and entropy
Discuss examples of natural processes in terms of
entropy changes.
Subsystems of the universe (like the freezing of
water into an ice cube) may have a decrease in
entropy, but overall the entropy of the whole
universe is increasing.
Topic 10: Thermal physics
10.3 The second law and entropy
Discuss examples of natural processes in terms of
entropy changes.
A phase change of freezing makes for –Q so that
the entropy decreases for the wax.
Since the air gains a corresponding Q its entropy
increases.