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Review of Thermodynamics
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1. How many "laws of thermodynamics" are there?
4
3
5
6
2. Suppose we have a binary system in which
N
= 6
, and
N
_{up}
= 3
. What is the multiplicity function?
2/3
20
120
Need more information
3. If the multiplicity function is 100 for particular values of
N
and
N
_{up}
in a binary system, what is the probability of being in any particular state?
1/100
100
1/50
0.001
4. The multiplicative factor that relates the fundamental and conventional temperatures is known as:
The Boltzmann Factor
The Multiplicity Function
The Boltzmann Constant
The Boltzmann Distribution
5. The average value of a property A is given by:
A
(
s
)
A
(
s
)
g
P
(
s
) +
A
(
s
)
None of the above
6. Take a two state system. If the probability of being in the first state of energy
= 0
is 0.75 and the probability of being in the second state of energy
= 100
Joules is 0.25, then what is
U
?
100
75
25
25
7. Which of the following correctly relates the entropy to the multiplicity function?
σ
= log
_{10}
g
σ
= log
_{e}
g
σ
= 10
^{g}
σ
=
e
^{g}
8. Which gives the correct definition of the temperature?
=
τ
=
=
τ
=
9. What are the SI units of the fundamental entropy?
Joules
No units
Joules/Kelvin
It depends on the system.
10. Which law of thermodynamics says that heat is a form of energy?
1st
2nd
3rd
4th
11. Which of the following is not an intensive variable?
Pressure
Temperature
Entropy
Chemical Potential
12. The energy U is intended to be a function of how many variables?
6
3
3
1
13. The expression

σ
dτ
+
V
dp
+
μ
dN
is equivalent to which of the following?
dH
dF
dU
dG
14. We can define the Helmholtz free energy by:
F
=
U
+
τσ
F
=
U

τσ
F
=
U
+
τ
dσ
F
=
U

τ
dσ
15. The expression

is equivalent to which of the following?

V

τ
V
τ
16. Which is an expression of
τ
?


17. What are the SI units of the chemical potential?
Kelvin
No Units
Joules per Square Meter
Joules
18. Which is a correct formulation of the Gibbs free energy?
G
=
H
+
τσ
G
=
F

pV
G
=
U

τσ

pV
G
=
U

τσ
+
pV
19. Which of the following is a Maxwell relation?
= 
=
= 
=
20. Let us write an energy identity as
dENERGY
=
A
dB
+
C
dD
+
E
dF
, where we use the letters
A
through
F
to represent dummy variables that may occupy that spot in the expresssion. Which gives a formula for generating Maxwell relations?
=
=
=
=
21. A state has an energy of 0 and another state has energy
=
τ
. What is the ratio of the probability of finding the system in the first to that of finding it in the second?
e
e
^{1}
0
Not enough information
22. Calculate the partition function of the same system.
1 +
e
1 +
e
^{1}
23. What is the absolute probability of finding the system in the state of energy 0?
24. What is the free energy of this system?
F
=
τ
log (1 +
e
)
F
= 
τ
log (1 +
e
)
F
= 
τ
log (1 +
e
^{1}
)
F
=
τ
log (1 +
e
^{1}
)
25. At low temperatures, what does the Planck distribution function look like?
e
^{(μ)/τ}
e
^{(μ)/τ}
e
^{σ/τ}
e
^{σ/τ}
26. The radiant energy density for blackbody radiation goes as the temperature to what power?
1
2
3
4
27. The StefanBoltzmann law of radiation is expressed in terms of which of the following?
U
U
/
V
F
F
/
V
28. Consider a system that has three possible configurations. First, it may be unoccupied entirely. Second, it may have one particle in a state of energy 0. Third, it may have one particle in a state of energy
τ
. What is the Gibbs sum for this system?
λ
+
λ
^{1}
1 +
λ
+
λ
^{1}
1 + 2
λ
1 +
λ
+
λ
^{2}
29. What is the average occupancy of the orbital of energy 0?
1
1/
Z
_{G}
λ
/
Z
_{G}
(1 +
λ
)/
Z
_{G}
30. In the classical limit, the BoseEinstein distribution function becomes what?
f
=
f
=
e
^{(μ)/τ}
None of the above
31. The FermiDirac distribution function is expressed how?
f
=
f
=
e
^{(μ)/τ}
None of the above
32. Suppose that the
μ
=  2
τ
. What is the value of
λ
?
e
^{2}
e
^{2}
e
^{1/2}
e
^{1/2}
33. Suppose that
μ
=  2
τ
for some ideal gas. What must be the concentration of the gas be?
n
_{Q}
e
^{2}
n
_{Q}
e
^{2}
n
_{Q}
e
^{1/2}
n
_{Q}
e
^{1/2}
34. Which is a correct expression of the free energy of an ideal gas?
F
=
N
log
+
F
=
Nτ
log
F
=
Nμ

Nτ
None of the above
35. Which of the following choices gives a reasonable value for the air pressure in an average sized bedroom in SI units?
1
0.01
10000
100
36. What is the approximate entropy per unit volume of an ideal gas of concentration
n
_{Q}
?
n
_{Q}
/2
n
_{Q}
/3
n
_{Q}
2
n
_{Q}
37. Approximately how many moles of ideal gas are required for it to have an energy of 1 Joule at room temperature?
0.0003 moles
0.003 moles
0.03 moles
0.3 moles
38. What is the heat capacity at constant volume in SI units for one mole of ideal gas?
9
9×10
^{23}
3
3×10
^{23}
39. Suppose a particle is constrained to be in a plane. By equipartition, what is the energy of that particle?
τ
/2
τ
3
τ
/2
None of the above
40. Suppose that the Fermi energy of a Fermi gas is approximately
10
^{20}
Joules. What is the energy per mole of the ground state?
3600 Joules/mole
360 Joules/mole
36 Joules/mole
3.6 Joules/mole
41. Einstein condensation is:
The effect due to fermions crowding into the ground orbital.
The effect due to bosons occupying all of the orbitals below a certain energy level and leaving vacant all of the orbitals above that level.
The effect due to bosons crowding into the ground orbital.
The effect due to fermions occupying all of the orbitals below a certain energy level and leaving vacant all of the orbitals about that level.
42. Which is an expression of the Carnot efficiency of a heat engine?
W
/
Q
_{h}
43. Which of these pathways cannot be completely performer due to entropy considerations?
Work
→
Work
Heat
→
Work
Work
→
Heat
None of the above
44. Which of the following relationships is true for the entropy entering and leaving a real heat engine?
σ
_{l}
≥
σ
_{h}
σ
_{l}
≤
σ
_{h}
σ
_{l}
=
σ
_{h}
σ
_{l}
=
σ
_{h}
+
Q
_{h}
/
τ
_{h}
45. Which of the following relationships correctly relates the input and output heats in a heat engine?
Q
_{l}
≥
Q
_{h}
(
τ
_{h}
/
τ
_{l}
)
Q
_{l}
≥
Q
_{h}
Q
_{l}
≤
Q
_{h}
(
τ
_{l}
/
τ
_{h}
)
Q
_{l}
≥
Q
_{h}
(
τ
_{l}
/
τ
_{h}
)
46. Which device does not consume work to move heat?
Heat Engine
Refrigerator
Air Conditioner
Heat Pump
47. Which relation holds for refrigerators?
τ
_{h}
<
τ
_{l}
Q
_{h}
=
Q
_{l}
+
W
σ
_{h}
≤
σ
_{l}
Q
_{h}
≤
Q
_{l}
48. Picturing the Carnot cycle, what does
(
σ
_{H}

σ
_{L}
)
τ
_{h}
represent?
The efficiency of the engine
The work done by the engine
The heat consumed at
τ
_{h}
The heat unable to be converted into work
49. In the Carnot cycle, the expansion stage that moves from higher to lower temperature is what kind of process?
Isothermal
Isentropic
Isobaric
None of the above
50. Which energy is the most appropriate choice to analyze a process at constant pressure and temperature?
U
H
F
G
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