One mole of an ideal gas $\left( {\frac{{{C_p}}}{{{C_v}}} = Y} \right)$ heated by law $P = \alpha V$ where $P$ is pressure of gas, $V$ is volume, $\alpha $ is a constant. What is the molar heat capacity of gas in the process

Initial pressure and volume of a gas are $P$ and $V$ respectively. First it is expanded isothermally to volume $4\ V$ and then compressed adiabatically to volume $V.$ The final pressure of gas will be (given $\gamma = 3/2)$

A long cylindrical pipe of radius $20 \,cm$ is closed at its upper end and has an airtight piston of negligible mass as shown. When a $50 \,kg$ mass is attached to the other end of piston, it moves down by a distance $\Delta l$ before coming to equilibrium. Assuming air to be an ideal gas, $\Delta l / l$ (see figure) is close to $\left(g=10 \,m / s ^2\right.$, atmospheric pressure is $10^5 \,Pa$ ),

An insulated box containing a diatomic gas of molar mass $m$ is moving with velocity $v$. The box is suddenly stopped. The resulting change in temperature is :-

Three moles of an ideal monoatomic gas perform a cycle as shown in the figure. The gas temperature in different states are: $T_1 = 400\, K,\, T_2 = 800\, K,\, T_3 = 2400\, K$ and $T_4 = 1200\,K$ . The work done by the gas during the cycle is  …. $kJ$