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

In an adiabatic process,the initial and final temperatures of $1 \, mol$ of an ideal gas are $T_1$ and $T_2$ respectively. The change in internal energy of the gas is .......

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

At $27^\circ C$,a gas is suddenly compressed such that its pressure becomes $1/8$th of the original pressure. The temperature of the gas will be $(\gamma = 5/3)$.

$A$ van der Waals gas obeys the equation of state $\left(p+\frac{n^2 a}{V^2}\right)(V-n b)=n R T$. Its internal energy is given by $U=C T-\frac{n^2 a}{V}$. The equation of a quasistatic adiabat for this gas is given by

If $\Delta U$ and $\Delta W$ represent the increase in internal energy and work done by the system respectively in a thermodynamical process,which of the following is true?