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Two cylinders $A $ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at $300\ K.$ 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 $30\ K,$ then the rise in temperature of the gas in $B$ is ....... $K$
$30$
$18$
$50$
$42$
Solution
In both cylinders $A$ and $B$ the gases are diatomic $(Y=1.4) .$ Piston $A$ is free to move i.e. it is isobaric process. Piston $\mathrm{B}$ is fixed i.e. it is isochoric process. If same amount of heat $\Delta Q$ is given to both then
$(\Delta Q)_{\text {isobaric }}=(\Delta Q)_{\text {isochoric }}$
$\mu C_{p}(\Delta T)_{A}=\mu C_{v}(\Delta T)_{B}$
$(\Delta T)_{B}=\frac{C_{p}}{C_{v}}(\Delta T)_{A}$
$=\gamma(\Delta T)_{A}=1.4 \times 30=42 \mathrm{K}$
