Thermodynamics Question 301
Question: The efficiency of an ideal gas with adiabatic exponent $ ‘\gamma ’ $ for the shown cyclic process would be
Options:
A) $ \frac{( 2l\text{n}2-1 )}{\gamma /( \gamma -1 )} $
B) $ \frac{( 1-2l\text{n}2 )}{\gamma /( \gamma -1 )} $
C) $ \frac{( 2l\text{n}2+1 )}{\gamma /( \gamma -1 )} $
D) $ \frac{( 2l\text{n}2-1 )}{\gamma /( \gamma +1 )} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ W _{AB}=0,W _{BC}=P\Delta V=nR\Delta T=-nRT _{0} $
$ W _{CA}=nRT\ell n\frac{V _{f}}{V _{i}}=nR(2T _{0})\ell n2 $
$ Q _{BC}=nC _{p}\Delta T=( \frac{nR\gamma }{\gamma -1} )T _{0} $
$ \text{Efficieancy, }\eta =\frac{W}{Q}=[ \frac{2\ell n2-1}{\gamma /( \gamma -1 )} ] $
