A) \[\frac{b}{1+b}\]
B) \[b\]
C) \[\frac{b+1}{b+2}\]
D) \[1+\frac{1}{b}\]
Correct Answer: D
Solution :
As process is adiabatic, \[\Delta Q=0.\] |
\[\Rightarrow \]\[dU+pdV=0\] |
\[\Rightarrow \]\[d\,(a+bpV)+pdV=0\] |
\[\Rightarrow \]\[(b+1)\frac{dV}{V}=-b\frac{dp}{p}\] |
Integrating and rearranging, we get |
\[\Rightarrow \]\[(b+1)\ln V+b\ln p=\text{constant}\] |
\[\Rightarrow \]\[p{{V}^{\left( \frac{b+1}{b} \right)}}=a\,\text{constant}\] |
\[\Rightarrow \]\[\gamma =\frac{b+1}{b}=1+\frac{1}{b}\] |
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