A) 32
B) \[\frac{40}{3}\]
C) 8
D) same as before
Correct Answer: A
Solution :
For adiabatic process, the following relation holds \[P{{V}^{\gamma }}=\]constant where P is pressure, V the volume and\[\gamma \]the ratio of specific heat. Given, \[\gamma =\frac{5}{3},{{V}_{1}}=V,{{V}_{2}}=\frac{V}{8}\] \[{{P}_{1}}V_{1}^{\gamma }={{P}_{2}}V_{2}^{\gamma }\] \[\Rightarrow \] \[{{P}_{2}}={{P}_{1}}\frac{V_{1}^{\gamma }}{V_{2}^{\gamma }}\] \[{{P}_{2}}=P{{\left( \frac{8V}{V} \right)}^{5/3}}\] \[{{P}_{2}}={{2}^{5}}P=32P\] Hence, new pressure is 32 times the original pressure.
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