An ideal gas having initial pressure $P$, volume $V$ and temperature $T$ is allowed to expand adiabatically until its volume becomes $4V$, while its temperature falls to $T/2$. If the work done by the gas during the expansion is $\alpha PV$, the value of $\alpha$ is

Which of the following is the best container for a gas during an adiabatic process?

When an ideal diatomic gas undergoes adiabatic expansion,if the increase in its volume is $0.5 \%$,then the change in the pressure of the gas is

$A$ gas having $\gamma = 5/2$ and volume $360 \text{ c.c.}$ is suddenly compressed to $90 \text{ c.c.}$ If the initial pressure of the gas is $P$,then the final pressure will be:

$A$ monoatomic ideal gas,initially at temperature $T_1$,is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. If $L_1$ and $L_2$ are the lengths of the gas column before and after expansion respectively,then $T_1/T_2$ is given by

An ideal gas is found to obey $p V^{3/2} = \text{constant}$ during an adiabatic process. If such a gas initially at a temperature $T$ is adiabatically compressed to half of its initial volume, then its final temperature is