Figure shows a cylindrical adiabatic container of total volume $2V_0$ divided into two equal parts by a conducting piston (which is free to move). Each part containing identical gas at pressure $P_0$ . Initially temperature of left and right part is $4T_0$ and $T_0$ respectively. An external force is applied on the piston to keep the piston at rest. Find the value of external force required when thermal equilibrium is reached. ( $A =$ Area of piston)

A monatomic gas at pressure $P_1$ and volume $V_1$ is compressed adiabatically to ${\frac{1}{8}}^{th}$ of its original volume. What is the final pressure of the gas is ........ $P_1$?

One mole of an ideal gas $(\gamma = 1.4)$ is adiabatically compressed so that its temperature rises from $27\,^oC$ to $35\,^oC$ . The change in the internal energy of the gas is  .... $J$. (given $R = 8.3\,J/mole-K$ )

The initial pressure and volume of an ideal gas are $P_0$ and $V_0$. The final pressure of the gas when the gas is suddenly compressed to volume $\frac{ V _0}{4}$ will be (Given $\gamma=$ ratio of specific heats at constant pressure and at constant volume)

During the adiabatic expansion of $2$ moles of a gas, the internal energy of the gas is found to decrease by $2$ joules, the work done during the process on the gas will be equal to ....... $J$

Initial pressure and volume of a gas are $ P$ and $V$ respectively. First it is expanded isothermally to volume $4V$ and then compressed adiabatically to volume $ V$. The final pressure of gas will be