$A$ gas for which $\gamma = 1.5$ is suddenly compressed to $\frac{1}{4}$ of its initial volume. What is the ratio of the final pressure to the initial pressure?

The work of $146 \ kJ$ is performed in order to compress one kilo mole of gas adiabatically,and in this process,the temperature of the gas increases by $7 ^\circ C$. The gas is $(R = 8.3 \ J \ mol^{-1} K^{-1})$.

During an adiabatic process,the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of $\frac{C_p}{C_v}$ for the gas is:

One mole of an ideal gas $\left(\gamma = \frac{5}{3}\right)$ at $127^{\circ} C$ is compressed adiabatically to $\left(\frac{8}{27}\right)$ of its initial volume. Find the magnitude of the work done on the system in $cal$.

$5.6 \ L$ 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).

$A$ 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.