Transcript Slide 1
Chapter 12 The Laws of Thermodynamics
Heat and work
W
F
s
(
PA
)
s
P
(
A
s
)
P
V W
P
V
Thermodynamic cycle
Heat and work
•
Work is done by the system:
W
P
V
•
Work is done on the system :
W
P
V
The first law of thermodynamics
•
Work and heat are path-dependent quantities
•
Quantity
Q + W =
Δ
E
int
is path-independent ( change of internal energy )
•
1st law of thermodynamics : the internal energy of a system increases if heat is added to the system or work is done on the system
E
int
E
int,
f
E
int,
i
Q
W
The first law of thermodynamics
•
Adiabatic process: no heat transfer between the system and the environment
E
int 0
W
W
•
Isochoric
E
int
(constant volume) process
Q
0
Q
•
Free expansion :
•
E
int 0 0
Cyclical
E
int
process:
Q
W Q
W
0 0
Chapter 12 Problem 18 Consider the cyclic process depicted in the figure. If Q is negative for the process BC and ΔE int W, and ΔE int is negative for the process CA, what are the signs of Q, that are associated with each process?
Work done by an ideal gas at constant temperature
•
Isothermal process – a process at a constant temperature
PV
nRT P
(
nRT
) /
V
const
/
V
•
Work ( isothermal expansion )
W
nRT
ln
V f V i
Work done by an ideal gas at constant volume and constant pressure
•
Isochoric process – a process at a constant volume
W
P
V V f
V i
0
W
0 •
Isobaric process – a process at a constant pressure
W
P
V
Molar specific heat at constant volume
•
Heat related to temperature change:
Q
c V
(
nm
0
N A
)
T
nC V
T
•
Internal energy change:
E
int
C V
nC V
E
int
n
T
T
W
3
nRT
2
n
T nC V
T
3 2 0
R
T
T
nC V
T
3 2
R
E
int
nC V
T C V
3 2
R
12 .
5
J
/
mol
K
Molar specific heat at constant pressure
•
Heat related to temperature change:
Q
nC P
T
•
Internal energy change:
E
int
Q
W
nC P
T
P
V nC V
T
nC P
T
nR
T C P
C V
R
Free expansion of an ideal gas
E
int 0
T i
T f PV
nRT P i V i
P f V f
Time direction
•
Irreversible processes – processes that cannot be reversed by means of small changes in their environment
Configuration
•
Configuration – certain arrangement of objects in a system
•
Configuration for
N
spheres in the box, with
n
spheres in the left half
n N
n
Microstates
•
Microstate – one of the ways to prepare a configuration
•
An example of 4 different microstates for 4 spheres in the box, with 3 spheres in the left half
Multiplicity
•
Multiplicity (
W
) – a number of microstates available for a given configuration
•
From statistical mechanics:
W
n
!
(
N N
!
n
)!
N
!
1 2 ...
N
1
N
0 !
1
n N
n For example
: 5 !
1 2 3 4 5 120
Multiplicity
N
4 ;
n
4
W
4 !
4 !
( 4 4) !
24 24 1 1
Multiplicity
N
4 ;
n
3
W
4 !
3 !
( 4 3) !
24 6 1 4
Multiplicity
N
4 ;
n
2
W
4 !
2 !
( 4 2) !
24 2 2 6
Multiplicity
N
6
Entropy
•
For identical spheres all microstates are equally probable
•
Entropy (
S
), see the tombstone:
S
k B
ln
W
•
For a free expansion of 100 molecules
•
Entropy is growing for irreversible processes in isolated systems
Entropy
•
Entropy , loosely defined, is a measure of disorder the system in
•
Entropy is related to another fundamental concept – information . Alternative definition of irreversible processes – processes involving erasure of information
•
Entropy cannot noticeably decrease in isolated systems
•
Entropy has a tendency to increase in open systems
Entropy in open systems
•
In open systems entropy can decrease :
•
Chemical reactions
•
Molecular self-assembly
•
Creation of information
Entropy in thermodynamics
•
In thermodynamics, entropy for open systems is
S
Q T
•
For isothermal process, the change in entropy:
S
Q T
•
For adiabatic process, the change in entropy:
S
Q T
0
Q
0
The second law of thermodynamics
•
In closed systems , the entropy increases for irreversible processes and remains constant for reversible processes
S
0 •
In real (not idealized) closed systems the process are always irreversible to some extent because of friction, turbulence, etc.
•
Most real systems are open since it is difficult to create a perfect insulation
Engines
•
In an ideal engine , all processes are reversible and no wasteful energy transfers occur due to friction, turbulence, etc.
•
Carnot engine :
Nicolas Léonard Sadi Carnot (1796 –1832)
Carnot engine (continued)
•
Carnot engine on the p-V diagram:
W
|
Q h
| |
Q c
| •
Carnot engine on the T-S diagram:
S
S
S h
0
S c
|
Q h T h
| |
Q h
|
T h Q c T c
| | |
Q c T c
|
Engine efficiency
•
Efficiency of an engine ( ε):
e
Energy we get Energy we pay for
|
W
|
Q h
| |
e C
•
For Carnot engine:
| |
W Q h
| | |
Q h
| | |
Q c Q h
| | 1 |
Q
|
Q h c
| |
e C
1
T T h c
|
Q h
|
T h
|
Q c T c
|
Perfect engine
•
Perfect engine :
•
For a perfect Carnot engine:
e C
1 1
T T h c
T T h c
0
T c
0
T h
•
No perfect engine is possible in which a heat from a thermal reservoir will be completely converted to work
Gasoline engine
•
Another example of an efficient engine is a gasoline engine :
Chapter 12 Problem 31 In one cycle, a heat engine absorbs 500 J from a high-temperature reservoir and expels 300 J to a low-temperature reservoir. If the efficiency of this engine is 60% of the efficiency of a Carnot engine, what is the ratio of the low temperature to the high temperature in the Carnot engine?
Heat pumps (refrigerators)
•
In an ideal refrigerator , all processes are reversible and no wasteful energy transfers occur due to friction, turbulence, etc.
•
Performance of a refrigerator (K):
K
What we want What we pay for
|
Q c
|
W
| | •
For Carnot refrigerator :
K C
|
Q h
| |
Q c
| |
Q c
|
T h T c
T c
Perfect refrigerator
•
Perfect refrigerator :
•
For a perfect Carnot refrigerator:
S
|
Q T c
| |
Q
|
T h T h
T c
S
0 •
No perfect refrigerator is possible in which a heat from a thermal reservoir with a lower temperature will be completely transferred to a thermal reservoir with a higher temperature
Questions?
Answers to the even-numbered problems Chapter 12 Problem 36 6.06 kJ/K
Answers to the even-numbered problems Chapter 12 Problem 56 (a) −4.9 × 10 −2 J (b) 16 kJ (c) 16 kJ