$A$ perfect gas is found to obey the relation $PV^{3/2} =$ constant,during an adiabatic process. If such a gas,initially at a temperature $T$,is compressed adiabatically to half its initial volume,then its final temperature will be

One mole of an ideal monatomic gas undergoes a process described by the equation $PV^3 = \text{constant}$. The heat capacity of the gas during this process 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

The variation of pressure $P$ with volume $V$ for an ideal diatomic gas is parabolic as shown in the figure. The molar specific heat of the gas during this process is

In a process,temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation $VT = K$,where $K$ is a constant. In this process,the temperature of the gas is increased by $\Delta T$. The amount of heat absorbed by the gas is ($R$ is the gas constant).

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