A) 8
B) 24
C) 32
D) 40
Correct Answer: C
Solution :
Given: Initial volume of the gas \[{{V}_{1}}=V\] Final volume of the gas \[{{V}_{2}}=\frac{V}{8}\] The relation for adiabatic change is given by \[{{P}_{1}}V_{1}^{\gamma }={{P}_{2}}V_{2}^{\gamma }\] \[\frac{{{P}_{2}}}{{{V}_{1}}}={{\left( \frac{{{V}_{1}}}{{{V}_{2}}} \right)}^{\gamma }}={{\left( \frac{V}{\frac{V}{8}} \right)}^{\gamma }}\] \[={{(8)}^{5/3}}={{2}^{5}}=32\]
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