LECTURE 11
SECOND LAW OF THERMODYNAMICS
Lecture instructor: Kazumi Tolich
Lecture 11
2
¨
Reading chapter 18.5 to 18.10
¤ The
second law of thermodynamics
¤ Heat engines
¤ Refrigerators
¤ Air conditions
¤ Heat pumps
¤ Entropy
Second law of thermodynamics
3
¨
The second law of thermodynamics states:
Thermal energy flows spontaneously from higher to lower temperature.
Heat engines are always less than 100% efficient at using thermal energy to do
work.
The total entropy of all the participants in any physical process cannot decrease
during that process.
Heat engines
4
¨
¨
Heat engines depend on the spontaneous heat flow from hot to
cold to do work.
In each cycle, the hot reservoir supplies heat 𝑄" to the engine
which does work 𝑊and exhausts heat 𝑄$ to the cold reservoir.
𝑊 = 𝑄" − 𝑄$
¨
The energy efficiency of a heat engine is given by
𝑒=
𝑊
𝑄"
Carnot’s theorem and maximum efficiency
5
¨
The maximum-efficiency heat engine is described in Carnot’s theorem:
If an engine operating between two constant-temperature reservoirs is to have maximum
efficiency, it must be an engine in which all processes are reversible. In addition, all reversible
engines operating between the same two temperatures, 𝑇$ and 𝑇" , have the same efficiency.
¨
This is an idealization; no real engine can be perfectly reversible.
¨
The maximum efficiency of a heat engine (Carnot engine) can be written as:
𝑒*+, = 1 −
𝑇$
𝑇"
Quiz: 1
6
¨
Consider the heat engine at right. 𝑄. denotes the
heat extracted from the hot reservoir, and 𝑄/
denotes the heat exhausted to the cold reservoir in
one cycle. What is the work done by this engine in
one cycle in Joules?
Quiz: 11-1 answer
7
¨
¨
4000 J
𝑊 = 𝑄. − 𝑄/ = 8000 J − 4000 J = 4000 J
Quiz: 2
8
¨
What kind of engine is this?
A.
B.
C.
a reversible (Carnot) heat engine
an irreversible heat engine
a hoax
Quiz: 11-2 answer
9
¨
An irreversible engine
¨
The efficiency of this engine: 𝑒 = 5 = :888 9 = 0.5
¨
The maximum efficiency this engine could have based on the temperatures of the hot and cold reservoirs:
4
7888 9
6
𝑒*+, = 1 −
=>
=6
=
?@8 A
B88 A
= 0.55
¨
Since 𝑒*+, > 𝑒, this is an irreversible engine.
¨
If 𝑒*+, = 𝑒, this would have been a reversible engine.
¨
If 𝑒*+, < 𝑒, this would have been a hoax.
Refrigerators, air conditions, and heat pump
10
¨
¨
Refrigerators, air conditioners, and heat pumps all use
work to transfer heat from a cold object to a hot object:
𝑄" = 𝑊 + 𝑄$
The coefficient of performance, COP: of refrigerators is
COP =
¨
𝑄$
𝑊
The COP for a heat pump is
COP =
𝑄"
𝑊
Quiz: 3
11
¨
In an ideal heat pump with two operating temperatures, cold 𝑇$ and hot 𝑇" , what is
the work needed add heat 𝑄" to a room?
A.
𝑄" 1 −
B.
𝑄"
C.
𝑄" 1 −
D.
𝑇"
𝑇$
E.
F.
=>
=6
=6
=>
=>
=6
Quiz: 11-3 answer
12
=>
¨ 𝑄" 1 −
=6
¨
In an ideal heat pump, the Carnot relationship holds:
¨
𝑄" = 𝑊 + 𝑄$
¨
𝑊 = 𝑄" − 𝑄$ = 𝑄" 1 −
5>
56
= 𝑄" 1 −
=>
=6
5>
56
=
=>
=6
Quiz: 4
13
¨
If you run a refrigerator in a thermally insulated room with the door to
the refrigerator open, the temperature of the room
A.
B.
C.
D.
E.
increases.
remains the same.
decreases.
Any of these can happen depending on how efficient the refrigerator is.
Any of these can happen depending on the relative sizes of the room
and the refrigerator.
Quiz: 11-4 answer
14
¨
¨
¨
¨
¨
increases.
The origin of the work done on the engine is the
electric energy that you buy from the electric
company.
This work is converted into heat and added to the
kitchen.
More heat is dumped in the kitchen than extracted.
𝑄" = 𝑊 + 𝑄$
Kitchen
Kitchen
Example: 1
15
¨
A refrigerator with a coefficient of
performance of 1.75 absorbs
Qc = 3.45 × 104 J of heat from the
low temperature reservoir during each
cycle.
a)
b)
How much mechanical work is required
to operate the refrigerator for a
cycle?
How much heat does the refrigerator
discard to the high temperature
reservoir during each cycle?
Change in entropy
16
¨
¨
Entropy is a state function that is associated with the degree of disorder or the
quality of energy.
The change in entropy ∆𝑆 for a reversible system is given by
∆𝑆 =
¨
¨
𝑄
𝑇
The entropy of the universe remains the same during a reversible process.
All real processes must go in the direction of increasing entropy and are
irreversible.
¤
In the process on the right, the end state is less ordered than the initial state—the
separation between low and high temperature areas has been lost.
Quiz: 5
17
¨
We have established that this engine is an
irreversible heat engine. We have learned that the
change in entropy for a reversible system is given
5
by ∆𝑆 = . Can we calculate the change in entropy
=
of this engine during one cycle?
A.
Yes
B.
No
Quiz: 11-5 answer
18
¨
¨
¨
Yes
Since entropy is a state function, we can replace this irreversible process with two equivalent
reversible processes and calculate the difference in entropy.
In an irreversible heat engine, the entropy increases by ∆𝑆KLK+M = −
56
=6
+
5>
=>
>0
Example: 2
19
¨
On a winter day, a certain house
loses Q = 5.00 ×108 J of heat to
the outside (about 500,000 Btu).
What is the total change in
entropy due to this heat transfer
alone, assuming an average indoor
temperature of 21.0 ºC and an
average outdoor temperature of
5.00 ºC ?
Quiz: 6
20
¨
During which of the following processes does the entropy of the universe
increase?
A.
B.
C.
D.
Ice dropped in hot coffee makes chilly coffee.
A book falls onto a table.
A damped pendulum eventually comes to rest.
A Carnot engines does work on a piston in a cycle.
Quiz: 11-6 answer
21
¨
Ice dropped in hot coffee makes chilly coffee.
¨
A book falls onto a table.
¨
A damped pendulum eventually comes to rest.
¨
A Carnot engines does work on a piston in a cycle.
¨
¨
Entropy of the universe increases during irreversible process.
Conservation of energy would allow the reversing of all of these processes, but not the second
law of thermodynamics.
¤
¤
¤
Chilly coffee does not spontaneously separate into hot coffee and ice.
A book on the table does not spontaneously gather thermal energy and convert into kinetic energy and
then to gravitational potential energy to jump up.
A pendulum at equilibrium position does not spontaneously gather thermal energy to start swinging.
n
Creation of thermal energy is irreversible – you can never convert it all back to work.
Quiz: 7
22
¨
A growing leaf makes complex glucose molecules, C6H12O6, from simple
CO2 and H2O. Or the theory of evolution tells us that the life started as
simple single-cell creatures and evolved into complex organisms. Does it
mean that the 2nd law of thermodynamics is violated?
A.
B.
Yes
No
Quiz: 11-7 answer
23
¨
No
¨
In biological systems entropy often decreases.
¨
¨
But the second law of thermodynamics says that the total entropy in the universe
increases.
If you include the heat flow of sun’s radiant energy which is responsible for all the
lives on earth, the total entropy increases as it should.
Second law of thermodynamics and statistics
24
¨
Why is entropy of the universe always increasing?
¤ Increasing
disorganization is more statistically probable, and it takes
effort to organize.
n Suppose
you start with an organized deck of cards (numbers are in orders, and
suits are separated).
n After you randomly shuffle the cards, the cards are most likely disorganized.
n There are many ways to disorganize the cars, but there is only one way to
organize it.
¤ Blame
the second law of thermodynamics for your messy room.
Third law of thermodynamics
25
¨
The third law of thermodynamics:
It is impossible to lower the temperature of an object to absolute zero in a
finite number of steps.
¤
Temperatures as low as 4.5 × 10-10 K have been achieved in the laboratory, but
absolute zero will remain ever elusive.