final2010.solutions

final2010.solutions - Final, Physics 9HB, Tuesday, March....

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Final, Physics 9HB, Tuesday, March. 16, 2010 Name: Directions: Test is open book, open note. Please write your name on every page. If you think there is something missing from the test which you need, please ask Jeremy. Use the backside of the paper as needed. 1) Short answer, 40 pts, 5 pts each. Explain your reasoning in the space provided or on the back of the page. A)A refrigerator uses 100W of electricity and discards 600W into the kitchen. Its coefficient of performance is a) .17 b) .2 c) 5 d) 6 e) Other. f) Impossible to answer-violates energy conserv. 600W is discarded, with 100W of work done. So Q H = 600 W, and thus Q c = 500W = Q H – W – hence COP = 500/100 = 5 B) A certain gas of atomic fermions has spin 3/2 (four spin orientations). Compared to a gas of spin ½ fermions of the same density and mass, what is its Fermi temperature? All else being equal, the Fermi momentum will go as p F = (h/2)(6 ν /[ π #spin components]) 1/3 so that for the same mass and density T F (S=3/2)/T F (S=1/2) = (2/4) 2/3 =2 -2/3 =0.63 since T F ~ p F 2 C) Scientists in Iceland discover geothermal vents that produce abundant pressurized steam with a temperature of 300 0 C. Engineers construct a heat engine that uses this steam as a hot reservoir and a nearby glacier as a cold reservoir. The maximum possible efficiency of this engine is a) 300% b) 100% c) 52% d) 45% e) 22% f) other Ice is at 0 0 C = 273K, so max efficiency is (1-273/573) = 52% D) 100 g of water is slowly heated from 5 0 to 25 0 C. What is its change in entropy? (For water, c = 4186 J/(kg-K)) Δ S = mc dT/T = mc ln(T 2 /T 1 ) where T 1 ,T 2 Hence S = 0.1 kg x 4186 J/(kg-K) x ln(298/278) = 29 J/K T 1 T 2
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E) A sample of He gas is held at constant temperature while it I s slowly compressed in a cylinder until its volume has decreased by a factor of 4. During this time the gas’s entropy a) increases b) decreases c) does not change d) does something else (explain). Decreases.
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final2010.solutions - Final, Physics 9HB, Tuesday, March....

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