A) \[\frac{2{{P}_{0}}}{3}\]
B) \[\frac{{{P}_{0}}}{3}\]
C) \[{{P}_{0}}\]
D) \[\frac{4{{P}_{0}}}{3}\]
Correct Answer: A
Solution :
[a] : Ideal gas equation \[PV=nRT\] \[({{P}_{0}}+(1-\alpha ){{V}^{2}})V=nRT\] \[T=\frac{({{P}_{0}}+(1-\alpha ){{V}^{2}})V}{nR}\] \[\frac{dT}{dV}=\frac{{{P}_{0}}}{nR}+\frac{3{{V}^{2}}(1-\alpha )}{nR}=0\] [For maximum temperature] \[{{P}_{0}}=3(\alpha -1){{V}^{2}}\]or\[{{V}^{2}}=\frac{{{P}_{0}}}{3(\alpha -1)}\] \[\therefore \]\[P={{P}_{0}}+(1-\alpha )\frac{{{P}_{0}}}{3(\alpha -1)}={{P}_{0}}-\frac{{{P}_{0}}}{3}=\frac{2{{P}_{0}}}{3}\]
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