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 = ΔEint (change of internal energy)
is path-independent
• 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
Eint  Eint, f  Eint,i  Q  W
The first law of thermodynamics
• Adiabatic process: no heat transfer between the
system and the environment
Eint  0  W  W
• Isochoric (constant volume) process
Eint  Q  0  Q
• Free expansion:
Eint  0  0  0
• Cyclical process:
Eint  Q  W  0
Q  W
Chapter 12
Problem 18
Consider the cyclic process depicted in the figure. If Q is negative for the
process BC and ΔEint is negative for the process CA, what are the signs of Q,
W, and ΔEint 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
Vf
Vi
Work done by an ideal gas at constant
volume and constant pressure
• Isochoric process – a process at a constant volume
W  PV  0
V f Vi
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  cV (nm0 N A )T  nCV T
• Internal energy change:
Eint  nCV T  W  nCV T  0  nCV T
3

 nRT 
Eint
3 RT 3
2


CV 

 R

nT
2 T
2
nT
Eint  nCV T
3
CV  R  12.5 J / mol  K
2
Molar specific heat at constant pressure
• Heat related to temperature change:
Q  nCP T
• Internal energy change:
Eint  Q  W  nCP T  PV
nCV T  nCP T  nRT
CP  CV  R
Free expansion of an ideal gas
Eint  0
Ti  T f
PV  nRT
PiVi  Pf 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:
N!
W
n!( N  n)!
n
N n
N! 1 2  ... N  1 N
0! 1
For exam ple:
5! 1 2  3  4  5  120
Multiplicity
N  4; n  4
4!
24
W

1
4! (4 - 4)! 24 1
Multiplicity
N  4; n  3
4!
24
W

4
3! (4 - 3)! 6 1
Multiplicity
N  4; n  2
4!
24
W

6
2! (4 - 2)! 2  2
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 in
the system
• 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
Q
S 
T
• For isothermal process, the change in entropy:
Q
S 
T
• For adiabatic process, the change in entropy:
Q
S 
0
T
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 | Qh |  | Qc |
• Carnot engine on the T-S diagram:
| Qh | | Qc |
S  Sh  Sc 

Th
Tc
| Qh | | Qc |

S  0 
Th
Tc
Engine efficiency
• Efficiency of an engine (ε):
Energywe get
|W |
e

Energywe pay for | Qh |
• For Carnot engine:
| Qc |
| W | | Qh |  | Qc |
eC 

 1
| Qh |
| Qh |
| Qh |
Tc
eC  1 
Th
| Qh | | Qc |

Th
Tc
Perfect engine
• Perfect engine:
• For a perfect Carnot engine:
Tc
eC  1  1 
Th
Tc  0
Tc
 0
Th
Th  
• 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):
| Qc |
What we want
K

What we pay for | W |
• For Carnot refrigerator :
| Qc |
Tc
KC 

| Qh |  | Qc | Th  Tc
Perfect refrigerator
• Perfect refrigerator:
• For a perfect Carnot refrigerator:
|Q| |Q|
S  

Tc
Th
Th  Tc  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