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(D) $1$. For a complete cycle,the net change in internal energy is zero: $\Delta U_{A \rightarrow B} + \Delta U_{B \rightarrow C} + \Delta U_{C \right

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(D) $1$. For a complete cycle,the net change in internal energy is zero: $\Delta U_{A ightarrow B} + \Delta U_{B ightarrow C} + \Delta U_{C ightarrow A} = 0$.$2$. For process $B ightarrow C$ (isochoric),work done $W_{B ightarrow C} = 0$. Thus,$\Delta U_{B ightarrow C} = Q_{B ightarrow C} = - 500 	ext{ kJ}$.$3$. For process $A ightarrow B$ (isobaric),$W_{A ightarrow B} = P \Delta V = (3 	imes 10^5 	ext{ Pa}) 	imes (1.5 - 1) 	ext{ m}^3 = 1.5 	imes 10^5 	ext{ J} = 150 	ext{ kJ}$.$4$. From the first law,$Q_{A ightarrow B} = \Delta U_{A ightarrow B} + W_{A ightarrow B} = 400 + 150 = 550 	ext{ kJ}$.$5$. For process $C ightarrow A$,$W_{C ightarrow A} = 	ext{Area under } CA = \frac{1}{2} 	imes (1.5 - 1) 	imes (3 	imes 10^5 - 2 	imes 10^5) = \frac{1}{2} 	imes 0.5 	imes 10^5 = 0.25 	imes 10^5 	ext{ J} = 25 	ext{ kJ}$. Since volume decreases,$W_{C ightarrow A} = - 25 	ext{ kJ}$.$6$. $\Delta U_{C ightarrow A} = - (\Delta U_{A ightarrow B} + \Delta U_{B ightarrow C}) = - (400 - 500) = + 100 	ext{ kJ}$.$7$. $Q_{C ightarrow A} = \Delta U_{C ightarrow A} + W_{C ightarrow A} = 100 - 25 = 75 	ext{ kJ}$. Note: Re-evaluating the cycle,the provided options seem inconsistent with standard calculation. Given the constraints,if we assume the question implies a specific result,we select the closest logical path.

Column $I$	Column $II$
$A$. Ratio of $\frac{\Delta Q}{\Delta U}$ in an isobaric process	$1$. $\frac{T_1}{T_1-T_2}$
$B$. Ratio of $\frac{\Delta Q}{\Delta W}$ in an isobaric process	$2$. $\frac{T_2}{T_1-T_2}$
$C$. Coefficient of performance of a refrigerator	$3$. $\frac{\gamma}{\gamma-1}$
$D$. Coefficient of performance of a heat pump	$4$. $\gamma$

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