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(D) For an ideal diatomic gas,the molar heat capacity at constant pressure is $C_p$ and at constant volume is $C_v$. The ratio is given by $\gamma = \

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$42$

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(D) For an ideal diatomic gas,the molar heat capacity at constant pressure is $C_p$ and at constant volume is $C_v$. The ratio is given by $\gamma = \frac{C_p}{C_v} = 1.4$.In cylinder $A$,the piston is free to move,so the process is isobaric (constant pressure). The heat supplied is $\Delta Q = \mu C_p (\Delta T)_A$.In cylinder $B$,the piston is fixed,so the process is isochoric (constant volume). The heat supplied is $\Delta Q = \mu C_v (\Delta T)_B$.Since the same amount of heat is given to both,we have $\mu C_p (\Delta T)_A = \mu C_v (\Delta T)_B$.Rearranging for $(\Delta T)_B$,we get $(\Delta T)_B = \frac{C_p}{C_v} (\Delta T)_A = \gamma (\Delta T)_A$.Substituting the given values: $(\Delta T)_B = 1.4 	imes 30 \ K = 42 \ K$.

Column-$1$	Column-$2$
$P$: Process-$I$	$A$: Adiabatic
$Q$: Process-$II$	$B$: Isobaric
$R$: Process-$III$	$C$: Isochoric
$S$: Process-$IV$	$D$: Isothermal

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