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) .

The volume of $1\; mole$ of an ideal gas with the adiabatic exponent $\gamma$ is changed according to the relation $V=\frac bT$ where $b =$ constant. The amount of heat absorbed by the gas in the process if the temperature is increased by $\triangle T$ will be

In an adiabatic process, the density of a diatomic gas becomes $32$ times its initial value. The final pressure of the gas is found to be $n$ times the initial pressure. The value of $n$ is

Following figure shows $P-T$ graph for four processes $A, B, C$ and $D$. Select the correct alternative.

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement $1:$ In an adiabatic process, change in internal energy of a gas is equal to work done on/by the gas in the process.

Statement $2 :$ The temperature of a gas remains constant in an adiabatic process.