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(C) $(I)$ $\Delta Q = mL = 10^{-3} 	imes 2250 	imes 10^3 \, J = 2250 \, J = 2.25 \, kJ$. Work done $\Delta W = P\Delta V = 10^5 	imes (10^{-3} - 10

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$I \rightarrow P, II \rightarrow R, III \rightarrow T, IV \rightarrow Q$

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(C) $(I)$ $\Delta Q = mL = 10^{-3} 	imes 2250 	imes 10^3 \, J = 2250 \, J = 2.25 \, kJ$. Work done $\Delta W = P\Delta V = 10^5 	imes (10^{-3} - 10^{-6}) \approx 10^5 	imes 10^{-3} = 100 \, J = 0.1 \, kJ$. $\Delta U = \Delta Q - \Delta W = 2.25 - 0.1 = 2.15 \, kJ \approx 2 \, kJ$ $(P)$.$(II)$ For isobaric expansion, $\Delta U = nC_v\Delta T$. For diatomic gas, $C_v = \frac{5}{2}R$. Since $V \propto T$, $T_2 = 3T_1 = 1500 \, K$. $\Delta U = 0.2 	imes \frac{5}{2} 	imes 8 	imes (1500 - 500) = 0.2 	imes 20 	imes 1000 = 4000 \, J = 4 \, kJ$ $(R)$.$(III)$ For adiabatic process, $PV^{\gamma} = 	ext{constant}$. For monatomic gas, $\gamma = 5/3$. $P_2 = P_1(V_1/V_2)^{\gamma} = 2 	imes (8)^{5/3} = 2 	imes 32 = 64 \, kPa$. $\Delta U = nC_v\Delta T = \frac{3}{2}(P_2V_2 - P_1V_1) = \frac{3}{2}(64 	imes \frac{1}{24} - 2 	imes \frac{1}{3}) = \frac{3}{2}(\frac{8}{3} - \frac{2}{3}) = \frac{3}{2} 	imes 2 = 3 \, kJ$ $(T)$.$(IV)$ For diatomic gas with vibration, $C_p = \frac{9}{2}R$ and $C_v = \frac{7}{2}R$. $\Delta Q = nC_p\Delta T = 9 \, kJ$. $\Delta U = nC_v\Delta T = \frac{C_v}{C_p} \Delta Q = \frac{7/2}{9/2} 	imes 9 = 7 \, kJ$ $(Q)$.

$List-I$	$List-II$
$(I)$ $10^{-3} \, kg$ of water at $100^{\circ} C$ is converted to steam at the same temperature, at a pressure of $10^5 \, Pa$. The volume of the system changes from $10^{-6} \, m^3$ to $10^{-3} \, m^3$. Latent heat of water $= 2250 \, kJ/kg$.	$(P)$ $2 \, kJ$
$(II)$ $0.2 \, moles$ of a rigid diatomic ideal gas with volume $V$ at temperature $500 \, K$ undergoes an isobaric expansion to volume $3V$. Assume $R = 8.0 \, J \, mol^{-1} \, K^{-1}$.	$(Q)$ $7 \, kJ$
$(III)$ One mole of a monatomic ideal gas is compressed adiabatically from volume $V = 1/3 \, m^3$ and pressure $2 \, kPa$ to volume $V/8$.	$(R)$ $4 \, kJ$
$(IV)$ Three moles of a diatomic ideal gas whose molecules can vibrate, is given $9 \, kJ$ of heat and undergoes isobaric expansion.	$(S)$ $5 \, kJ$
	$(T)$ $3 \, kJ$

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