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(C) For an ideal diatomic gas, the molar heat capacity at constant volume is $C_V = \frac{5}{2}R$ and at constant pressure is $C_P = \frac{7}{2}R$.In

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$45$

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(C) For an ideal diatomic gas, the molar heat capacity at constant volume is $C_V = \frac{5}{2}R$ and at constant pressure is $C_P = \frac{7}{2}R$.In cylinder $B$, the piston is fixed, so the process is isochoric (constant volume). The heat supplied is $Q = n C_V \Delta T_B$.In cylinder $A$, the piston is free to move, so the process is isobaric (constant pressure). The heat supplied is $Q = n C_P \Delta T_A$.Since the same amount of heat is given to both, we have $n C_V \Delta T_B = n C_P \Delta T_A$.Substituting the values: $C_V \Delta T_B = C_P \Delta T_A$.$\frac{5}{2}R 	imes 63 = \frac{7}{2}R 	imes \Delta T_A$.$5 	imes 63 = 7 	imes \Delta T_A$.$\Delta T_A = \frac{5 	imes 63}{7} = 5 	imes 9 = 45 	ext{ K}$.

List-$I$	List-$II$
$A$. Isothermal Process	$I$. Work done by the gas decreases internal energy
$B$. Adiabatic Process	$II$. No change in internal energy
$C$. Isochoric Process	$III$. The heat absorbed goes partly to increase internal energy and partly to do work
$D$. Isobaric Process	$IV$. No work is done on or by the gas

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