A) \[P{{V}^{3/2}}\]= constant
B) \[P{{V}^{5/2}}\]= constant
C) \[P{{V}^{7/3}}\]= constant
D) \[P{{V}^{4/3}}\]= constant
Correct Answer: A
Solution :
\[T{{V}^{\gamma -1}}\]= constant \ \[\frac{{{T}_{1}}}{{{T}_{2}}}={{\left( \frac{{{V}_{2}}}{{{V}_{1}}} \right)}^{\gamma -1}}\]or \[{{\left( \frac{1}{2} \right)}^{\gamma -1}}=\sqrt{\frac{1}{2}}\] \ \[\gamma -1=\frac{1}{2}\]or \[\gamma =\frac{3}{2}\] \ \[P{{V}^{3/2}}\]= constant
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