An ideal gas at atmospheric pressure is adiabatically compressed so that its density becomes $32$ times of its initial value. If the final pressure of gas is $128$ atmosphers, the value of $\gamma$ the gas is

$Assertion :$ Adiabatic expansion is always accompanied by fall in temperature.
$Reason :$ In adiabatic process, volume is inversely proportional to temperature.

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

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)

Starting with the same initial conditions, an ideal gas expands from volume $V_{1}$ to $V_{2}$ in three different ways. The work done by the gas is $W_{1}$ if the process is purely isothermal. $W _{2}$. if the process is purely adiabatic and $W _{3}$ if the process is purely isobaric. Then, choose the coned option