hw16 - – 1 – Solutions to Homework Problem Set 16 1....

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Unformatted text preview: – 1 – Solutions to Homework Problem Set 16 1. Find the efficiency of the Carnot cycle in terms of T h and T l . From the class notes, the total work done throughout the Carnot cycle is W = RT h ln V 2 V 1 + RT l ln V 4 V 3 , and heat is absorbed only during the isothermal expansion stage as Q h = RT h ln V 2 V 1 . The efficiency is defined as η = W Q h . Also noting that the 2nd and 4th stages are adiabatic, we may relate V 2 and V 3 and V 1 and V 4 using the adiabatic relation TV γ- 1 = const. . For the 2nd stage of adia- batic expansion, T 2 V γ- 1 2 = T 3 V γ- 1 3 , thus V 3 = V 2 ( T 2 /T 3 ) 1 / ( γ- 1) = V 2 (( T h /T l ) 1 / ( γ- 1) . In the same way, for the last stage of adiabatic compression, T 4 V γ- 1 4 = T 1 V γ- 1 1 , so V 4 = V 1 ( T 1 /T 4 ) 1 / ( γ- 1) = V 1 ( T h /T l ) 1 / ( γ- 1) . Replacing V 3 and V 4 in the expressions of η , we get η = ( RT h ln V 2 V 1 + RT l ln V 4 V 3 ) / ( RT h ln V 2 V 1 ) = ( RT h ln V 2 V 1- RT l ln V 2 V 1 ) / ( RT h ln V...
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This note was uploaded on 03/17/2012 for the course PHYS 204 taught by Professor Atkin during the Spring '12 term at Amity University.

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hw16 - – 1 – Solutions to Homework Problem Set 16 1....

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