Two moles of helium gas $\left(\gamma = \frac{5}{3}\right)$ at $27^{\circ} C$ is expanded at constant pressure until its volume is doubled. Then it undergoes an adiabatic change until the temperature returns to its initial value. The work done during the adiabatic process is (universal gas constant $R = 8.3 \ J \ mol^{-1} \ K^{-1}$) (in $J$)

$A$ cyclic process $ABCD$ is shown in the given $P-V$ diagram. Which of the following diagrams represents the same process in a $P-T$ graph?

An office room contains about $2000$ moles of air. The change in the internal energy of this much air when it is cooled from $34^{\circ} C$ to $24^{\circ} C$ at a constant pressure of $1.0 \text{ atm}$ is (Use $\gamma_{\text{air}} = 1.4$ and universal gas constant $R = 8.314 \text{ J/mol-K}$)

Two cylinders $A$ and $B$ fitted with pistons contain an equal amount of an ideal rigid diatomic gas at $303 \ K$. The piston of cylinder $A$ is free to move,and that of cylinder $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in cylinder $B$ is $49 \ K$,then the rise in temperature of the gas in $A$ is: (in $K$)

Which of the following quantities does not characterize the thermodynamic state of a substance?

Three processes form a thermodynamic cycle as shown on the $P-V$ diagram for an ideal gas. Process $1 \rightarrow 2$ takes place at a constant temperature $(300 \ K)$. Process $2 \rightarrow 3$ takes place at a constant volume. During this process,$40 \ J$ of heat leaves the system. Process $3 \rightarrow 1$ is adiabatic and the temperature $T_3$ is $275 \ K$. The work done by the gas during the process $3 \rightarrow 1$ is ..... $J$.