A) \[\frac{1}{\gamma }\]
B) \[\left( 1-\frac{1}{\gamma } \right)\]
C) \[\gamma -1\]
D) \[\left( 1-\frac{1}{{{\gamma }^{2}}} \right)\]
Correct Answer: B
Solution :
\[\frac{dW}{dQ}=\frac{dQ-dU}{dQ}\] \[\Rightarrow \] \[\frac{dW}{dQ}=1-\frac{dU}{dQ}\] \[\Rightarrow \] \[\frac{dW}{dQ}=1-\frac{n{{C}_{V}}dT}{n{{C}_{p}}dT}\] \[\Rightarrow \] \[\frac{dW}{dQ}=1-\frac{{{C}_{V}}}{{{C}_{p}}}=1-\frac{1}{\gamma }\]
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