An ideal rigid diatomic gas $(\gamma = 7/5)$ undergoes an adiabatic change. If the relation between temperature and volume is $TV^x = \text{constant}$, then the value of $x$ is:

An ideal gas at $27^{\circ}C$ is compressed adiabatically to $\frac{8}{27}$ of its original volume. If $\gamma = \frac{5}{3}$,then the rise in temperature is ........ $K$.

The amount of work done in an adiabatic expansion from temperature $T$ to ${T_1}$ is

$A$ gas is suddenly compressed to one fourth of its original volume. What will be its final pressure,if its initial pressure is $P$?

The pressure and density of a given mass of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$ change adiabatically from $(P, d)$ to $(P^{\prime}, d^{\prime})$. If $\frac{d^{\prime}}{d} = 32$, then $\frac{P^{\prime}}{P}$ is $(\gamma = \text{ratio of specific heats})$.

During a thermodynamic process, the increase in internal energy of a system is equal to the work done on the system. Which process does the system undergo?