Sp09-MT1-Huang-Soln

Sp09-MT1-Huang-Soln - Problem 3 Part A: In this...

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Unformatted text preview: Problem 3 Part A: In this configuration, the heat output of the first engine is the heat input of the second engine. Let e 1 = 1 2 ( 1- T 2 T 1 ) and e 2 = 1 2 ( 1- T 4 T 3 ) be the efficiencies of the first and second engines respectively. Note that each engine is operating at 50% of its Carnot efficiency, as stated in the problem. Q H 1 = W 1 + Q L 1 W 1 = e 1 · Q H 1 ⇒ Q L 1 = ( 1- e 1 ) · Q H 1 W 2 = e 2 · Q H 2 = e 2 · Q L 1 = e 2 · ( 1- e 1 ) · Q H 1 W total = W 1 + W 2 = ( e 1 + e 2- e 1 · e 2 ) Q H 1 Let r be the rate at which coal is being burned. Then Δ Q H 1 Δ t = rb . p = Δ W total Δ t = ( e 1 + e 2- e 1 · e 2 ) · Δ Q H 1 Δ t ⇒ p = ( e 1 + e 2- e 1 · e 2 ) · rb ⇒ r = p ( e 1 + e 2- e 1 · e 2 ) · b = 122 kg s Part B: For this part, we’ll look at the engine as a whole and apply the first law of thermodynamics. Q in = W + Q out ⇒ Δ Q in Δ t = Δ W Δ t + Δ Q out Δ t ⇒ rb = p + Δ Q out Δ t = p + Δ Q W Δ t ⇒ Δ Q W Δ t = rb- p = 2665 MW Part C: 1 Q = mc Δ T ⇒ Δ Q W Δ t = Δ m Δ t c W Δ T ⇒ Δ m Δ t = Δ Q W Δ t m W Δ T = 106000 kg s 2 1 1 Huang, Spring 2009 Problem 4 (25 points) An ideal monoatomic gas in a thermally insulated box is separated by a thermally conducting partition into two parts. There are n moles of gas in each part. Initially the gas in part A has temperature T 1 and ovlume V 1 and in B temperature T 2 and volume V 2 . The partition can slide without friction and the two parts have the same pressure, P . (a) (10 pts.) What is the final temperature when thermal equilibrium is reached?...
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This note was uploaded on 02/09/2010 for the course PHYSICS 7B taught by Professor Packard during the Spring '08 term at University of California, Berkeley.

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Sp09-MT1-Huang-Soln - Problem 3 Part A: In this...

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