VII. The second low of Thermodynamics
1. Reversible and irreversible processes
•Mechanics
•Thermodynamics
Heat can flow spontaneously from a hot object to a cold object;
heat will not flow spontaneously from a cold object to a hot object.
2. Heat engines
•H.E. transforms heat partly into work or mechanical energy
•Working substance
•Cycle process: ΔU = 0
ΔU = Q - W = 0
efficiency:
W = Q = QH + QC = |QH| - |QC|
QC
W

 1
QH
QH
3. Refrigerators
coefficient of
performance:
QC
QC
k

W
QH  QC
TH
|QH|
engine
|QC|
TC
W
4. The second law of thermodynamics and heat engines
It is impossible to build a heat engine with 100% efficiency
5. The Carnot Cycle (reversible)
QC
TC

QH
TH
a
P
Maximum efficiency:
TC TH  TC
C  1

TH
TH
b
TH
d
c
TL
TC
kC 
TH  TC
V
6. The Carnot Cycle and the second law of thermodynamics
No device is possible whose sole effect is to transform a given amount of
heat completely into work
No device is possible whose sole effect is to transform heat from one system
at temperature TL into a second system at higher temperature TH
Example 1: A nuclear power plant generate steam at 6300 C.
The steam is sent through a series of turbines and exits at 1000 C.
What is the maximum possible efficiency of the power station?
TH = 630ºC
TC = 100ºC
εC - ?
TH  TC
C 
TH
630 C  630 C  273.15  903.15K
100 C  100 C  273.15  373.15K
(630  100) K
C 
 0.59
903.15K
 C  59%
Example 2: An ice-making machine operates in a Carnot cycle.
It takes heat from water at 0.0C and rejects heat to a room at 24.0C.
Suppose that 50.0 kg of water at 0.0C are converted to ice at 0.0C.
How much energy must be supplied to the device?
Heat of fusion of water is 334*103 J/kg.
Q  mL
TH = 24.0C
TC = 0.0C
QC
TC
kC 

W
TH  TC
m = 50.0 kg
L = 334*103 J/kg
W-?
TH  TC
TH  TC
W  QC
 mL
TC
TC
(24.0  0.0) K
W  50.0kg  334 10 J / kg
 1.47 106 J
273.15K
3
Question
In one cycle, a heat engine does
10 J of work and exhausts 20 J of
waste heat.
The thermal efficiency of the heat
engine is ___ %.
1.
2.
3.
4.
0
20
33
50
W  QH  QC

W
W
10 J


 0.33
QH W  QC 10 J  20 J
  33%
Question
In a Carnot heat engine, the cold
temperature reservoir is at 300 K
(= 27 ˚C) and the thermal
efficiency is 50%.
1.
2.
3.
4.
The temperature of the hot reservoir is
___ K.
TC
C  1
TH
TC
 1 C
TH
400
600
800
1000
TH  TC 1   C 
TH  300K 1  0.5  600K
Question
A refrigerator has a coefficient of
performance K = 2.00. Work is
done on the refrigerator at a rate
Pwork = dW/dt = 100 Watts.
1.
2.
3.
4.
The rate at which heat is removed
from inside the refrigerator is d|QC|/dt
= ___ Watts.
QC
k
W
QC  k W
d QC
dt
k
dW
d QC
dt
dt
 200 Watts
50
100
200
400
The internal-combustion engine
• A fuel vapor can be compressed, then detonated
to rebound the cylinder, doing useful work.
6. Otto cycle
QC
W

 1
QH
QH
 Otto  1 
1
r  1
r - compression ratio
γ – CP/CV
Example: An automobile engine
has a compression ratio of 10.0.
The maximum theoretical
thermal efficiency of the
engine is ___ %.
( = 1.40 for air)
 Otto  1 
1
10
1.4 1
 0.60  60%