Answers are given at the end of the exam
	
PHYS 352 Spring 1999
	Exam 1
									mult. choice:_______
 									prob 1:      ________
									prob 2:      ________

									TOTAL:     ________

Name ____________________					February 23, 1999
	Please Print

You are expected to observe the GMU honor code.  Please read these instructions carefully:
1. You may be pressed for time, so don't waste time on things you get stuck on.
2. There's no penalty for guessing on the multiple choice part, so don't leave any blank.
3. Multiple choice questions count 4 points each, for a total of 60 points for that part.
4. Be sure to read each question VERY carefully.  Experience shows that a major reason people answer questions wrong is that they don't read them correctly.

			  

						

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1. At what Celsius temperature is the temperature in Celsius equal to half the temperature in Kelvin?
(a) 156 C,  (b) 373 C,  (c) 273 C,  (d) 100 C,   (e) none of the above

2. A certain blackbody radiates 100 watts of power when its temperature is T.  How many watts would it radiate if its temperature were 2T?
(a) 200 w,  (b) 400 w,  (c) 800 w,  (d) 1600 w,  (e) none of the above

3. How much does the entropy of the universe change when 1000 J of heat flows through a metal bar, one end of which is maintained at 500 K, and the other end at 400 K?
(a) +550 J/0K,  (b) -550 J/0K,  (c) +50 J/0K,  (d) -50 J/0K,  (e) none of the above

4. Suppose you put m grams of a substance having a specific heat equal to one tenth that of water into 5m grams of water.  What is the final equilibrium temperature if the initial temperatures of the substance and water are 100 C and 0 C respectively?
(a) 1.96 C,  (b) 2.44 C,  (c) 5.00 C,  (d) 50.0 C, (e) none of the above

5. You can get badly burned from steam, because water has a very high:
(a) specific heat,  (b) latent heat of fusion,  (c) latent heat of vaporization,
(d) thermal expansion coefficient,  (e) none of the above

6. How many calories are needed to completely boil away 1 kg of water initially at 0 C?
(a) 640 cal,  (b) 540 cal,  (c) 100 cal,  (d) 320 cal,  (e) none of the above

7. What is the expected value of the ratio CP/CV for a diatomic gas at room temperature?  What does its value become at very low temperatures?
(a) 1.67, 1.4 at low T,  (b) 1.4, 1.67 at low T,  (c) 1.67, 1.67 at low T, (d) 1.4, 1.4 at low T, 

8. Under what conditions does the equation: CP - CV = R hold?
(a) only for monatomic gases, (b) only for diatomic gases,  (c) only for ideal gases,
(d) none of the above

9. During which steps of the Carnot cycle is Q = 0?  During which steps is ΔU = 0?  (AB and CD are isotherms, and BC and DA are adiabatics.)
(a) Q = 0 and ΔU = 0 during AB and CD,
(b) Q = 0 and ΔU = 0 during BC and DA,
(c) Q = 0 for AB & CD, ΔU = 0 for BC & DA, 
(d) Q = 0 for BC & DA, ΔU = 0 for AB & CD
(e) none of the above

10. At what altitude is the atmospheric density and pressure equal to half their surface values, assuming no variation in temperature?  
(a) kT/mg,  (b) mg/kT,  (c) kT ln2/mg,  (d) mg ln2/kT,  (e) none of the above

11. Two gases A and B are in equilibrium.  If the molecules of A have four times the mass of those of B, what is the ratio of the rms speeds vA/vB?
(a) 0.5,  (b) 2,  (c) 0.25,  (d) 4,  (e) none of the above

12. Between 0 C and 4 C, water has a negative value of:
(a) specific heat,  (b) latent heat of fusion,  (c) latent heat of vaporization,
(d) thermal expansion coefficient,  (e) none of the above

13. The furnace of your home needs to put out 1000 watts of heat on a continuous basis to keep the inside at a steady 70 F when its 30 F outside.  Suppose the R-value of your insulation were doubled in all the walls, windows, and roof, and the thermostat were turned down to 60 F instead of 70 F.  How many watts would the furnace now need to put out when its 30 F outside?
(a) 425 w,  (b) 375 w,  (c) 225 w,  (d) 500 w,  (e) none of the above

14. A Carnot engine
(a) was built by Carnot during the last century
(b) is approximated by a gasoline engine
(c) operates on an Otto cycle
(d) is an idealization of the most efficient possible engine operating between TH and TC
(e) none of the above

15. What happens to the absolute pressure in a gas if its volume is halved, and its absolute temperature doubles?
(a) no change,  (b) it quadruples,  (c) it doubles,  (d) it is a quarter as much, (e) none

Problem 1

15 pts (a) To keep a nuclear reactor cool 105 kg/s of water are pumped through it and dumped back in a lake, after the water temperature has been raised by 10 C.  Find the efficiency of the plant if its power output is 1000 Mw = 109 w.

8 pts (b) What would be the maximum possible efficiency of such a reactor be if it produces high pressure steam at 800 K to run the turbines and expels the waste heat at 400 K?

7 pts (c) Why is the water that flows through the reactor to cool it kept under very high pressure?

Problem 2.  Consider the cycle ABCA shown, where AB is an isotherm
										     A
	B
										     C
12 pts (a) Starting from basic definitions, find the work done during the complete cycle expressed in terms of PB, VA, VB, and n.

6 pts (b) during which part(s) of the cycle is Q > 0?  During which part(s) is Q < 0?

6 pts (c) Find TC if TA = 600 K and VB = 2VA.

6 pts (d) What is the value of ΔU and ΔS for the entire cycle?

1. (c)
2. (d)
3. (e) I goofed.  The correct ans is +0.5 J/K
4. (a) 
5. (c)
6. (a)
7. (b)
8. (c)
9. (d)
10. – forget it book skipped this topic.
11. (a)
12. (d)
13. (b)
14. (d)
15. (b)

prob. 1(a)  Each second Qc = mcdT = (10^5)(4186)(10) = 4.186 GJ
			W = 10^9 J = 1GJ, 
		so Qh = 5.186 GJ, and e = W/Qh = 0.19 (19%)

 (b) e = 1 – Tc/Th = 1 – 400/800 = 0.5  (50%)

(c) Because otherwise it would turn to steam.  Steam is not nearly as effective as water for cooling purposes, given the smaller mass in contact with the reactor at any given moment.

Prob 2 (a) area under the isotherm from A to B is W = Int (P dV) = Int (nRT dV/V) 
= nRT ln (Vb/Va), but we need to subtract Pb(Vb – Va) for the portion of the cycle ba,
giving:  nRT ln (Vb/Va) – pb(Vb – Va)

(b) Q = dU + W > 0 during ab
during b  c, W < 0 and dU < 0, so Q < 0
during c  a W = 0 and dU > 0, so Q >0

(c) Use ideal gas law giving Tc = Tb (Pc/Pb)(Vc/Vb) = 300 K
(d) both are zero, because both are state variables.