An ideal gas follows a process described by the equation $PV^2 = C$ from the initial $(P_1, V_1, T_1)$ to final $(P_2, V_2, T_2)$ thermodynamic states,where $C$ is a constant. Then:

An ideal gas undergoes a quasi-static,reversible process in which its molar heat capacity $C$ remains constant. If during this process the relation of pressure $P$ and volume $V$ is given by $PV^n = \text{constant}$,then $n$ is given by (Here $C_p$ and $C_v$ are molar specific heat at constant pressure and constant volume,respectively):

The specific heat of a gas in a polytropic process is given by

$A$ gas obeys $P^2V = \text{constant}$. The initial temperature and volume are $T_0$ and $V_0$. If the gas expands to a volume of $2V_0$,the final temperature is:

An ideal gas expands according to the law $P^2 V = \text{constant}$. The internal energy of the gas

An ideal gas is found to obey $Pv^{\frac{3}{2}} = \text{constant}$ during an adiabatic process. If such a gas initially at a temperature $T$ is adiabatically compressed to $\frac{1}{4}$th of its volume,then its final temperature is