Question

An ideal monoatomic gas is enclosed in a non-conducting cylinder having a piston which can move freely. Suddenly the gas is compressed to 1/8 of its initial volume. Find the final pressure and temperature if initial pressure and temperature are $P_0$ and $T_0$ respectively.

Answer 1

Since process is adiabatic therefore
$P_0{V}^{\frac{5}{3}}=P_{final}{\left(\frac{V}{8}\right)}^{\frac{5}{3}}[\gamma =\frac{C_P}{C_V}=\frac{5R}{2}/\frac{3R}{2}=\frac{5}{3}]$
$P_{final}=32P_0$
Since process is adiabatic therefore
$T_1{V}_1^{\gamma -1}=T_2{V}_2^{\gamma -1}\Rightarrow T_0{V}_0^{2/3}=T_{final}{\left(\frac{V_0}{8}\right)}^{2/3}\Rightarrow T=4T_0$