A) \[\frac{(2\,\,\text{ln}\,2-1)}{\gamma /(\gamma -1)}\]
B) \[\frac{(1-2\,\,\text{ln}\,2)}{\gamma /(\gamma -1)}\]
C) \[\frac{(2\,\,\text{ln}\,2+1)}{\gamma /(\gamma -1)}\]
D) \[\frac{(2\,\,\text{ln}\,\,2-1)}{\gamma /(\gamma +1)}\]
Correct Answer: A
Solution :
[a] \[{{W}_{AB}}=0,\]\[{{W}_{BC}}=P\Delta V=nR\Delta T=-nR{{T}_{0}}\] \[{{W}_{CA}}=nRT\ell n\frac{{{V}_{f}}}{{{V}_{i}}}=nR\left( 2{{T}_{0}} \right)\ell n2\] \[{{Q}_{BC}}=n{{C}_{p}}\Delta T=\left( \frac{nR\gamma }{\gamma -1} \right){{T}_{0}}\] Efficiency, \[\eta =\frac{W}{Q}=\left[ \frac{2\ell n2-1}{\gamma /(\gamma -1)} \right]\]
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