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Two cylinders $A$ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at $300 \mathrm{~K}$. The piston of $A$ is free to move while that of $B$ 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 $A$ is $30 \mathrm{~K}$, then the rise in temperature of the gas in $B$ is
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$42 K$
In both cylinders $A$ and $B$ the gases are diatomic $(\gamma=1.4)$. Piston $A$ is free to move i.e. it is isobaric process. Piston $B$ is fixed i.e. it is isochoric process. If same amount of heat $\Delta Q$ is given to both then
$\begin{aligned} & (\Delta Q)_{\text {isobaric }}=(\Delta Q)_{\text {isochoric }} \Rightarrow \mu C_p(\Delta T)_A=\mu C_v(\Delta T)_B \\ & (\Delta T)_B=\frac{C_p}{C_v}(\Delta T)_A=\gamma(\Delta T)_A=1.4 \times 30=42 \mathrm{~K} . \\ & \end{aligned}$
$\begin{aligned} & (\Delta Q)_{\text {isobaric }}=(\Delta Q)_{\text {isochoric }} \Rightarrow \mu C_p(\Delta T)_A=\mu C_v(\Delta T)_B \\ & (\Delta T)_B=\frac{C_p}{C_v}(\Delta T)_A=\gamma(\Delta T)_A=1.4 \times 30=42 \mathrm{~K} . \\ & \end{aligned}$
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