PS3KEYF07 - Chemistry 391 PS3 KEY Fall 2007 1 a wab...

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1 Chemistry 391 Fall 2007 PS3 KEY 1. a) ( ) ( ) , , ln ln b ab hot a bc V m cold hot d cd cold c da V m hot cold bc V w nRT V w nC T T V w nRT V w nC T T w = − = = − = = − b) ln ln b d total hot cold a c V V w nRT nRT V V = − c) Use the adiabat relations for ideal gas: 1 1 1 1 c 1 1 1 1 and Solve these for / and equate the results, . Therefore, or Therefore ln cold hot b hot a cold d cold hot cold b a b a c b hot c d c d d a b total hot cold a T V T V T V T V T T T V V V V V V T V V V V V V V w nRT nRT V γ γ γ γ γ γ γ γ = = = = = = = − ( ) ln ln d b hot cold c a V V nR T T V V = − d) The heat withdrawn from the hot reservoir (isothermal process) where 0 ab U Δ = must be ln b ab ab hot a V q w nRT V = − = e) The efficiency is ( ) 1 1. cycle hot cold cold ab hot hot w T T T e q T T = = = <
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2 2. a) First calculate V c and V d . 1 1 1 1 3 5 2 1 3 1 1 1 1 5 1 3 ; 423 K 423 K 2.9649; 10.000 L*2.9649 29.649 L 873 K 873 K ; 423 K 423 K 873 K 873 K c c c c b b b b c c b d d d d a a a a d a T V V T T V V T V V V T V V T T V V T V V γ γ γ
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