Two cylinders $A$ and $B$ fitted with pistons contain equal amount of an ideal diatomic gas at $303 \text{ K}$. 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 $63 \text{ K}$, then the rise in temperature of the gas in $A$ is: (in $\text{ K}$)

Two moles of monoatomic gas is expanded from $(P_0, V_0)$ to $(P_0, 2V_0)$ under isobaric condition. Let $\Delta Q_1$,$\Delta W_1$,and $\Delta U_1$ be the heat given to the gas,the work done by the gas,and the change in internal energy,respectively. Now,the monoatomic gas is replaced by a diatomic gas,with other conditions remaining the same. The corresponding values in this case are $\Delta Q_2$,$\Delta W_2$,and $\Delta U_2$. Then:

One mole of a monoatomic gas and one mole of a diatomic gas are initially in the same state. Both gases are expanded isothermally and then adiabatically,such that they acquire the same final state. Choose the correct statement.

During the melting of a slab of ice at $273 \, K$ at atmospheric pressure,

One mole of a monatomic ideal gas is taken along two cyclic processes $E \rightarrow F \rightarrow G \rightarrow E$ and $E \rightarrow F \rightarrow H \rightarrow E$ as shown in the $PV$ diagram. The processes involved are purely isochoric,isobaric,isothermal,or adiabatic. Match the paths in List-$I$ with the magnitudes of the work done in List-$II$ and select the correct answer using the codes given below the lists.

List-$I$	List-$II$
$P. \quad G \rightarrow E$	$1. \quad 160 P_0 V_0 \ln 2$
$Q. \quad G \rightarrow H$	$2. \quad 36 P_0 V_0$
$R. \quad F \rightarrow H$	$3. \quad 24 P_0 V_0$
$S. \quad F \rightarrow G$	$4. \quad 31 P_0 V_0$

Codes: $P \quad Q \quad R \quad S$

The specific heat of hydrogen gas at constant pressure is $C_P = 3.4 \times 10^3 \text{ cal/kg } ^oC$ and at constant volume is $C_V = 2.4 \times 10^3 \text{ cal/kg } ^oC$. If $1 \text{ kg}$ of hydrogen gas is heated from $10^oC$ to $20^oC$ at constant pressure,the external work done by the gas is: