A) \[\frac{b+1}{b}\]
B) \[\frac{b+1}{a}\]
C) \[\frac{a+1}{b}\]
D) \[\frac{a}{a+b}\]
Correct Answer: A
Solution :
[a] \[U=a+bPV\] ?.(i) In adiabatic change, \[dU=-dW=\frac{nR}{\gamma -1}\left( {{T}_{2}}-{{T}_{1}} \right)=\frac{nR}{\gamma -1}\left( dT \right)\] \[\Rightarrow U=\int_{{}}^{{}}{dU}=\frac{nR}{\gamma -1}\int_{{}}^{{}}{dT}\] \[orU=\left( \frac{nR}{\gamma -1} \right)T+a=\frac{PV}{\gamma -1}+a\] ?(ii) Where a is the constant of integration. Comparing (1) and (2), we get \[b=\frac{1}{\gamma -1}\Rightarrow \gamma =\frac{b+1}{b}.\]
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