Quiz

1. Thermodynamics and Statistical
Mechanics
Review for Quiz 1

2. Thermo & Stat Mech - Spring 2006
Class 11 2
Laws of Thermodynamics
First law: đQ – đW = dU
Energy is conserved

3. Thermo & Stat Mech - Spring 2006
Class 11 3
Laws of Thermodynamics
Second Law: The entropy of an isolated
system increases in any irreversible process
and is unaltered in any reversible process.
This is the principle of increasing entropy.
DS  0

4. Thermo & Stat Mech - Spring 2006
Class 11 4
Laws of Thermodynamics
Third Law: The entropy of a true equilibrium
state of a system at a temperature of absolute
zero is zero.
Equivalent to: It is impossible to reduce the
temperature of a system to absolute zero
using a finite number of processes.

5. Thermo & Stat Mech - Spring 2006
Class 11 5
Second Law Variations
No series of processes is possible whose sole
result is the absorption of heat from a thermal
reservoir and the complete conversion of this
energy to work.
There are no perfect engines!

6. Thermo & Stat Mech - Spring 2006
Class 11 6
Second Law Variations
No series of processes is possible whose sole
result is the transfer of heat from a reservoir at
a given temperature to a reservoir at a higher
temperature.
There are no perfect refrigerators!

7. Thermo & Stat Mech - Spring 2006
Class 11 7
Zeroth Law
If two systems are separately in thermal
equilibrium with a third system, they are
in thermal equilibrium with each other.

8. Thermo & Stat Mech - Spring 2006
Class 11 8
Work done by a gas





f
i
V
V
PdV
W
PdV
dW
Ads
A
F
dW
Fds
dW

9. Thermo & Stat Mech - Spring 2006
Class 11 9
Ideal gas law
Ideal gas law: PV = nRT
In terms of molar volume, v = V/n,
this becomes:
Pv = RT, or P = RT/v

10. Thermo & Stat Mech - Spring 2006
Class 11 10
van der Waals equation of state
  RT
b
v
v
a
P
v
a
b
v
RT
P







 



2
2
or
,
Then,
This equation has a critical value of T which
suggests a phase change. The next slide shows
graphs for several values of T .

11. Thermo & Stat Mech - Spring 2006
Class 11 11
Thermal Expansion
Expansivity or Coefficient of Volume
Expansion, b.
T
V
T
T
V
V
P
T
T
v
v
T
V
V
P
P
P
D

D









D


















b
b
b
)
,
(
1
1

12. Thermo & Stat Mech - Spring 2006
Class 11 12
Compressibility
Volume also depends on pressure.
Isothermal Compressibility:
P
V
P
P
V
V
P
T
P
V
V
T
T
D


D









D












 )
,
(
1

13. Thermo & Stat Mech - Spring 2006
Class 11 13
Cyclical Relation
1
0














































































P
V
T
V
T
P
V
T
P
V
T
T
P
P
V
T
P
P
V
T
V
T
P
P
V
T
V

14. Thermo & Stat Mech - Spring 2006
Class 11 14
Carnot Cycle
A Carnot cycle is an idealized reversible cycle
that operates between two heat reservoirs at
temperatures T1 and T2, where T2 > T1. It can
operate as a heat engine, or a refrigerator.

15. Thermo & Stat Mech - Spring 2006
Class 11 15
Thermal Efficiency (h)
2
1
2
2
1
2
1
2
1
2
2
1
1
T
T
T
T
T
Q
Q
Q
Q
Q
Q
W









h
h
If T1 = 0, h = 1 (100%)

16. Thermo & Stat Mech - Spring 2006
Class 11 16
For a Carnot Engine
T
Q
T
T
Q
Q


1
2
1
2
1
2
1
2
T
T
Q
Q


or 0
2
2
1
1


T
Q
T
Q

17. Thermo & Stat Mech - Spring 2006
Class 11 17
Entropy
0

 
 T
Q
d
T
Q
d
i i
i
dS
T
Q
d

For reversible processes.
Entropy is a state variable.

18. Thermo & Stat Mech - Spring 2006
Class 11 18
First and Second Laws
First Law: dU = đQ – đW
First law, combined with the second law:
dU = TdS – PdV

19. Thermo & Stat Mech - Spring 2006
Class 11 19
Tds Equations
dP
c
dv
v
c
dP
P
T
c
dv
v
T
c
Tds
dP
Tv
dT
c
dP
T
v
T
dT
c
Tds
dv
T
dT
c
dv
T
P
T
dT
c
Tds
v
P
v
v
P
P
P
P
P
v
v
v
b

b
b

b













































20. Thermo & Stat Mech - Spring 2006
Class 11 20
Ideal Gas
R
c
c
T
Pv
P
T
Tv
c
c
Tv
c
c
v
p
v
p
v
p







2
2
1

b

21. Thermo & Stat Mech - Spring 2006
Class 11 21
Properties
From first law: TdS = dU + PdV, or
Internal Energy dU = TdS – PdV U(S, V)
Enthalpy: H = U + PV
dH = TdS + VdP H(S, P)

22. Thermo & Stat Mech - Spring 2006
Class 11 22
New Potentials
Helmholtz Function:
F = U – TS
Gibbs Function:
G = U – TS + PV
G = H – TS
G = F + PV

23. Thermo & Stat Mech - Spring 2006
Class 11 23
All Four
dU = TdS – PdV U(S, V)
dH = TdS + VdP H(S, P)
dF = – PdV – SdT F(V, T)
dG = – SdT + VdP G(T, P)

24. Thermo & Stat Mech - Spring 2006
Class 11 24
Maxwell Relations
P
T
P
S
V
T
V
S
T
V
P
S
S
V
P
T
T
P
V
S
S
P
V
T







































































25. Thermo & Stat Mech - Spring 2006
Class 11 25
Clausius-Clapeyron Equation
liquid
-
Solid
)
(
vapor
-
Solid
)
(
vapor
-
Liquid
)
(
12
12
13
13
23
23
v
v
T
dT
dP
v
v
T
dT
dP
v
v
T
dT
dP






































