This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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...
View
Full
Document
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.
 Spring '12
 atkin
 Work, Heat

Click to edit the document details