$5.6 \ L$ of helium gas at $STP$ is adiabatically compressed to $0.7 \ L$. If the initial temperature of the gas is $T \ K$,the work done in the process is ($R$ is the universal gas constant in $SI$ units).

$A$ 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

If the pressure in an adiabatic process increases by $\frac{2}{3}\%$,then the percentage decrease in volume will be ....... . Assume $C_P/C_V = 3/2$.

$A$ mass of diatomic gas $(\gamma = 1.4)$ at a pressure of $2 \text{ atm}$ is compressed adiabatically so that its temperature rises from $27^{\circ}C$ to $927^{\circ}C$. The pressure of the gas in the final state is ...... $\text{atm}$.

$A$ motor-car tyre has a pressure of $2\,atm$ at $27\,^{\circ}C$. It suddenly bursts. If $\gamma = (C_p/C_v) = 1.4$ for air,find the resulting temperature.