Physics 113 - Fall 00

Sample Final Exam Questions

1. The molar specific heat, c_{V}, of a block of iron at T = 1 K is

- c
_{V }< 3R - c
_{V }= 3R - c
_{V }> 3R

2. An __ideal Carnot engine__ acting as a refrigerator has one isothermal process in which Q_{food} joules of heat from the food is extracted in order to compress the working fluid of the refrigerator. The change of entropy of the working fluid, DS_{fluid}, is related to the change in entropy of the food, DS_{food}, by

- |DS
_{fluid }| > |DS_{food}| - |DS
_{fluid}|_{ }< |DS_{food}| - DS
_{fluid }= DS_{food}¹ 0 - DS
_{fluid }= - DS_{food} - DS
_{fluid }= DS_{food}= 0

3. A thermodynamic system has entropy *S *given by the expression . Here *U* is the internal energy, *V* the volume, *k* is Boltzmann's constant and *a* is a (different) constant. Which expression below gives the temperature of the system?

(a) *T *= *kaV/Ö
U*

(b) *T = Ö
U/ kaV*

(c) *T = kaVÖ
U*

4. Suppose an rubber band starts with a length of 10 cm and a temperature of 273^{o}K. Its state is changed in one of two ways:

i) The band is heated to a temperature of 290^{ }K. Then, being kept at this new temperature, it is slowly stretched until its length is 15 cm. In this entire process its entropy changes by an amount DS_{1}

ii) The band is slowly stretched to a length of 15 cm while being kept at a temperature of 273^{ }K. Then, while remaining at this length, it is slowly heated to 290^{ }K. In this entire process its entropy changes by an amount DS_{2.}

(a) DS_{1 }< DS_{2}

(b) DS_{1 }= DS_{2}

(c) DS_{1 }> DS_{2}

The next four questions pertain to the following figure:

A heat engine consists of 0.10 moles of an ideal monatomic gas that is confined to a cylinder with a piston. The gas is taken from state *X* to state *1,* to state *Z*, to state *2* and then back to state X*.* The *PV* diagram below shows the values of pressure and volume of the gas.

5. What is DU_{1}, the change in internal energy in the process *X®
1®
Z*?

*i.e.* DU_{1} = U(Z) - U(X).

a) DU_{1} < 0

b) DU_{1} = 0

c) DU_{1} > 0

6. What is W_{1}, the work done **by** the gas in the process *X®
1®
Z?*

a) W_{1} < 0

b) W_{1} = 0

c) W_{1} > 0

7. Compare |W_{2}|, the *absolute value* of the work done by the gas during process *Z®
2®
X* to |W_{1}|, the *absolute value* of the work done by the gas during process *X®
1®
Z*.

a) |W_{2}| < |W_{1}|

b) |W_{2}| = |W_{1}|

c) |W_{2}| > |W_{1}|

8. Now consider a different situation. Compare Q_{2}, the heat added to the gas during the __reverse process__ X®
2®
Z, with Q_{1}, the heat added to the gas during the __original process__ X®
1®
Z. (Consider the sign of the heat in your ranking such that all positive values are greater than all negative values, i.e., +4 > -8).

a) Q_{2} < Q_{1}

b) Q_{2} = Q_{1}

c) Q_{2} > Q_{1}

The next two questions pertain to the following situation:

In the atmosphere of a certain planet, the pressure at an altitude of 1 km is 1/2 that at the surface. The gravitational acceleration on the planet is 30 m/s^{2}, the atmosphere is made up entirely of nitrogen gas (m_{N2} = 4.64x10^{-26} kg) and is at a uniform temperature, *T*.

9. What is the temperature of the atmosphere *T*?

a) *T* = 48.5 K

b) *T* = 100.7 K

c) *T* = 146 K

d) *T* = 193 K

e) *T* = 226 K

10. Relative to the pressure, *p(0)*, at the surface, what is the pressure, p(5) an altitude of 5 km?

- p(5) = p(0)/5
- p(5) = p(0)/10
- p(5) = p(0)/32

11. The temperature of a summer day is 37 ^{o}C and the inside of your house is a comfortable 21 ^{o}C . A certain window in your house, 1 m x 0.5 m has a thickness of 5 cm. If the rate of heat flow into the house is 400 W, what is the thermal conductivity of the window, k?

(a) k = 0.05 W/m·K

(b) k = 0.125 W/m·K

(c) k = 0.75 W/m·K

(d) k = 1.25 W/m·K

(e) k = 2.5 W/m·K

12. Lead melts at 327 ^{o}C (at 1 atm pressure) and the latent heat of melting is 25 kJ/kg. At a temperature of 326 ^{o}C, what is the relation between the free energies, *F*, of solid and liquid lead?

(a) *G _{solid} > G_{liquid}*

(b) *G _{solid} = G_{liquid}*

(c) *G _{solid} < G_{liquid}*

13. A sample of SF_{6 }(sulfur hexafluoride) gas, initially with volume V_{i} = 0.1 m^{3} and temperature T_{i} = 250 K, expands adiabatically to V_{f} = 0.3 m^{3}. What is T_{f}, the final temperature of the SF_{6}? Assume that SF_{6} is an ideal gas.

14. What is *DS*, the change in the entropy of ten moles of an ideal monatomic gas that is expanded slowly and isothermally at a temperature of 293K from a pressure of 2 atm to a pressure of 1 atm?

(a) *DS* = 21.7 J/K

(b) *DS* = 57.6 J/K

(c) *DS* = 203.4 J/K

(d) *DS* = 212.6 J/K

(e) *DS* = 841 J/K

The next two questions pertain to the following situation:

Ten atoms are placed in a magnetic field. We will consider the effect of the magnetic field on the magnetic moments of the atoms. The magnitude of the "energy" difference between spin "up" atoms and spin "down" atoms is DM = 1.01 x 10^{-26} J/Tesla, and the magnetic field is pointing "up".

15. If the magnetic field is 1 Tesla and the temperature is 300 K, what is the ratio of probabilities, *R _{P}*, for a single atom to have its spin "up" relative "down"?

- 0.57
- 0.999998
- 1.000002
- 1.13
- 1.24

16. What is the average number of spin "up" atoms, *N _{up},* at temperature

- N
_{up}= 10e^{-}DMB/kT/(1+e^{-}DMB/kT) - N
_{up}= 10e^{-}DMB/kT - N
_{up}= 10e^{DMB/kT}/(1+e^{DMB/kT})

17. It has been proposed that we use H_{2} as our new energy source. H_{2} may be obtained from water by electrolysis. Which of the following most accurately and completely describes the status of this idea?

- It may allow for a very clean energy source.
- It requires major technical improvements to be economical.
- It would require technological improvements in the efficiency of electrolysis in order to be a net energy source.
- It has limited applicability due to the shortage of water.
- It would violate the laws of thermodynamics.

- The latent heat of the water-steam phase transition at p=1 atm and T=100
^{o}C is 2256 kJ/kg. What is the entropy change DS as the liquid vaporizes?

- –22.56 kJ/K-kg
- -6048 J/K-kg
- 0 J/K-kg
- 6048 J/K-kg
- 22.56 kJ/K-kg
- W = 172 J

19. The tray is continuously ‘jostled’, so that the 4 coins jump and flip randomly on the tray, causing all available ‘microstate’s of this system to become possible. What is the entropy of the 4 coin system in this "jostled" state?

a. s = 0

b. s = 1.4

c. s = 1.8

d. s = 2.1

e. s = 2.8

20. If the "jostling" is stopped, so that the 4 coins come to rest in a specific configuration of "heads" and "tails," what is the probability P that the 4 coin system will be found in its equilibrium configuration. I.e. 2 heads and 2 tails?

a. P = 0.125

b. P = 0.25

c. P = 0.375

d. P = 0.50

e. P = 0.625

The next 2 questions pertain to the following situation:

A balloon containing 0.25 mol of helium rises from an altitude at which the pressure is 90 kPa to an altitude at which the pressure is 67 kPa. During this ascent, the gas in the balloon maintains a constant temperature of 280 K.

*21. *How much work W does the gas in the balloon do during this process?

a. W = - 213 J

b. W = - 86 J

c. W = 0 J

d. W = 65 J

22. How much heat Q does the gas absorb during this process?

a. Q = -W

b. Q = 0

c. Q = W

23. Consider 1 mole of N_{2} gas at p = 1 atm in a volume of 1 liter. The gas undergoes an isothermal compression to a volume of 0.5 liters. Assuming that the N_{2} is an ideal gas, what is the change in entropy DS?

a. DS = 0

b. DS = 0.0823 l-atm/K

c. DS = -0.0570 l-atm/K

d. DS = -0.0823 l-atm/K

e. DS = -0.132 l-atm/K