1m³ of an ideal gas at 500 K and 1000 kPa expands reversibly to 5 times its initial volume in an insulated container. If the specific heat capacity (at constant pressure) of the gas is 21 J/mole.K, the final temperature will be

Solution(By Examveda Team)

Insulated cylinder $$ \Rightarrow $$   adiabatic system
$$\eqalign{ & \Rightarrow P{V^\gamma } = {\text{CONSTANT}} \cr & \Rightarrow T{V^{\gamma - 1}} = {\text{CONSTANT}} \cr & \Rightarrow \frac{{{T_1}}}{{{T_2}}} = \frac{{{V_2}^{\gamma - 1}}}{{{V_1}}} \cr & \Rightarrow \frac{{500}}{{{T_2}}} = {\left( 5 \right)^{\gamma - 1}} \cr & {C_P} - {C_V} = R\left( {{\text{For ideal gas}}} \right) \cr & \Rightarrow \gamma = 1.65 \cr & {\text{So, }}{T_2} = 176.05\,K \cr} $$