A van der Waal's 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

A gas ($\gamma = 1.3)$ is enclosed in an insulated vessel fitted with insulating piston at a pressure of ${10^5}\,N/{m^2}$. On suddenly pressing the piston the volume is reduced to half the initial volume. The final pressure of the gas is

A gas for which $\gamma = 1.5$ is suddenly compressed to $\frac{1}{4}$ th of the initial volume. Then the ratio of the final to the initial pressure is

In the following figure, four curves $A, B, C$ and $D$ are shown. The curves are

An iron rod of heat capacity $C$ is heated to temperature $8T_0$ . It is then put in a cylindrical vessel of adiabatic walls having two moles of air which can be treated as diatomic ideal gas at temperature $T_0$ and closed by a movable piston which is also adiabatic. The atmospheric pressure is $P_0$ .  The cylinder with the piston combined have heat capacity $2C$ . Find the equilibrium temperature . (Assume temperature of air to be uniform and equal to vessel at all times) .