An ideal gas mixture filled inside a balloon expands according to the relation $PV^{2/3} = \text{constant}$. The temperature inside the balloon is

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

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 $P-V$ diagram of a monoatomic gas is a straight line passing through the origin. The molar heat capacity of the gas in this process will be:

$A$ 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:

Consider one mole of an ideal gas in a cylindrical container following the path shown in the $P-V$ diagram. The process follows $PV^{1/2} = \text{constant}$.
$(a)$ Find the work done in taking the gas from state $1$ to state $2$.
$(b)$ If $V_2 = 2V_1$, what is the ratio of temperatures $\frac{T_1}{T_2}$?
$(c)$ The internal energy of one mole of gas at temperature $T$ is $\frac{3}{2}RT$. Find the heat supplied to the gas in taking it from state $1$ to state $2$.