SparkNotes: Review of Thermodynamics: Review Test

1. How many "laws of thermodynamics" are there?

(A) 4

(B) 3

(C) 5

(D) 6

2. Suppose we have a binary system in which N = 6, and N_up = 3. What is the multiplicity function?

(A) 2/3

(B) 20

(C) 120

(D) 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?

(A) 1/100

(B) 100

(C) 1/50

(D) 0.001

4. The multiplicative factor that relates the fundamental and conventional temperatures is known as:

(A) The Boltzmann Factor

(B) The Multiplicity Function

(C) The Boltzmann Constant

(D) The Boltzmann Distribution

5. The average value of a property A is given by:

(A)

A(s)

(B)

A(s)g

(C)

P(s) + A(s)

(D) 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?

(A) 100

(B) 75

(C) 25

(D) -25

7. Which of the following correctly relates the entropy to the multiplicity function?

(A) σ = log₁₀g

(B) σ = log_eg

(C) σ = 10^g

(D) σ = e^g

8. Which gives the correct definition of the temperature?

(A)

=

(B) τ =

(C)

=

(D) τ =

9. What are the SI units of the fundamental entropy?

(A) Joules

(B) No units

(C) Joules/Kelvin

(D) It depends on the system.

10. Which law of thermodynamics says that heat is a form of energy?

(A) 1st

(B) 2nd

(C) 3rd

(D) 4th

11. Which of the following is not an intensive variable?

(A) Pressure

(B) Temperature

(C) Entropy

(D) Chemical Potential

12. The energy U is intended to be a function of how many variables?

(A) 6

(B) 3

(C) 3

(D) 1

13. The expression - σ dτ + V dp + μ dN is equivalent to which of the following?

(A) dH

(B) dF

(C) dU

(D) dG

14. We can define the Helmholtz free energy by:

(A) F = U + τσ

(B) F = U - τσ

(C) F = U + τ dσ

(D) F = U - τ dσ

15. The expression -

is equivalent to which of the following?

(A) - V

(B) - τ

(C) V

(D) τ

16. Which is an expression of τ?

(A)

(B)

(C) -

(D) -

17. What are the SI units of the chemical potential?

(A) Kelvin

(B) No Units

(C) Joules per Square Meter

(D) Joules

18. Which is a correct formulation of the Gibbs free energy?

(A) G = H + τσ

(B) G = F - pV

(C) G = U - τσ - pV

(D) G = U - τσ + pV

19. Which of the following is a Maxwell relation?

(A)

= -

(B)

=

(C)

= -

(D)

=

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?

(A)

=

(B)

=

(C)

=

(D)

=

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?

(A) e

(B) e^-1

(C) 0

(D) Not enough information

22. Calculate the partition function of the same system.

(A) 1 + e

(B)

(C)

(D) 1 + e^-1

23. What is the absolute probability of finding the system in the state of energy 0?

(A)

(B)

(C)

(D)

24. What is the free energy of this system?

(A) F = τ log (1 + e)

(B) F = - τ log (1 + e)

(C) F = - τ log (1 + e^-1)

(D) F = τ log (1 + e^-1)

25. At low temperatures, what does the Planck distribution function look like?

(A) e^(
-μ)/τ

(B) e^(μ-
)/τ

(C) e^-
ω/τ

(D) e^ω/τ

26. The radiant energy density for blackbody radiation goes as the temperature to what power?

(A) 1

(B) 2

(C) 3

(D) 4

27. The Stefan-Boltzmann law of radiation is expressed in terms of which of the following?

(A) U

(B) U/V

(C) F

(D) 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?

(A) λ + λ^-1

(B) 1 + λ + λ^-1

(C) 1 + 2λ

(D) 1 + λ + λ²

29. What is the average occupancy of the orbital of energy 0?

(A) 1

(B) 1/Z_G

(C) λ/Z_G

(D) (1 + λ)/Z_G

30. In the classical limit, the Bose-Einstein distribution function becomes what?

(A) f =

(B) f =

(C) e^(
-μ)/τ

(D) None of the above

31. The Fermi-Dirac distribution function is expressed how?

(A) f =

(B) f =

(C) e^(
-μ)/τ

(D) None of the above

32. Suppose that the μ = - 2τ. What is the value of λ?

(A) e^-2

(B) e²

(C) e^-1/2

(D) e^1/2

33. Suppose that μ = - 2τ for some ideal gas. What must be the concentration of the gas be?

(A) n_Qe^-2

(B) n_Qe²

(C) n_Qe^-1/2

(D) n_Qe^1/2

34. Which is a correct expression of the free energy of an ideal gas?

(A) F = N

log

+

(B) F = Nτlog

(C) F = Nμ - Nτ

(D) 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?

(A) 1

(B) 0.01

(C) 10000

(D) 100

36. What is the approximate entropy per unit volume of an ideal gas of concentration

n_Q?

(A) n_Q/2

(B) n_Q/3

(C) n_Q

(D) 2n_Q

37. Approximately how many moles of ideal gas are required for it to have an energy of 1 Joule at room temperature?

(A) 0.0003 moles

(B) 0.003 moles

(C) 0.03 moles

(D) 0.3 moles

38. What is the heat capacity at constant volume in SI units for one mole of ideal gas?

(A) 9

(B) 9×10²³

(C) 3

(D) 3×10²³

39. Suppose a particle is constrained to be in a plane. By equipartition, what is the energy of that particle?

(A) τ/2

(B) τ

(C) 3τ/2

(D) 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?

(A) 3600 Joules/mole

(B) 360 Joules/mole

(C) 36 Joules/mole

(D) 3.6 Joules/mole

41. Einstein condensation is:

(A) The effect due to fermions crowding into the ground orbital.

(B) 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.

(C) The effect due to bosons crowding into the ground orbital.

(D) 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?

(A)

(B)

(C)

(D) W/Q_h

43. Which of these pathways cannot be completely performer due to entropy considerations?

(A) Work → Work

(B) Heat → Work

(C) Work → Heat

(D) None of the above

44. Which of the following relationships is true for the entropy entering and leaving a real heat engine?

(A) σ_l≥σ_h

(B) σ_l≤σ_h

(C) σ_l = σ_h

(D) 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?

(A) Q_l≥Q_h(τ_h/τ_l)

(B) Q_l≥Q_h

(C) Q_l≤Q_h(τ_l/τ_h)

(D) Q_l≥Q_h(τ_l/τ_h)

46. Which device does not consume work to move heat?

(A) Heat Engine

(B) Refrigerator

(C) Air Conditioner

(D) Heat Pump

47. Which relation holds for refrigerators?

(A) τ_h < τ_l

(B) Q_h = Q_l + W

(C) σ_h≤σ_l

(D) Q_h≤Q_l

48. Picturing the Carnot cycle, what does (σ_H - σ_L)τ_h represent?

(A) The efficiency of the engine

(B) The work done by the engine

(C) The heat consumed at τ_h

(D) 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?

(A) Isothermal

(B) Isentropic

(C) Isobaric

(D) None of the above

50. Which energy is the most appropriate choice to analyze a process at constant pressure and temperature?

(A) U

(B) H

(C) F

(D) G