A monatomic gas at pressure $P_1$ and volume $V_1$ is compressed adiabatically to ${\frac{1}{8}}^{th}$ of its original volume. What is the final pressure of the gas is ........ $P_1$?
AIPMT 2010, Medium
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Ideal gas equation, for an adiabatic process is
$PV' = constant\,or\,\,{P_1}V_1^\gamma = {P_2}V_2^\gamma $
$For\,monoatomic\,gas\,\gamma = \frac{5}{3}$
$\therefore \,\,{P_1}V_1^{5/3} = {P_2}{\left( {\frac{{{V_1}}}{8}} \right)^{5/3}}$
$ \Rightarrow \,{P_2} = {P_1} \times {\left( 2 \right)^5} = 32\,{P_1}.$
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