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 ..... $K$
IIT 1998,AIIMS 2019, Medium
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(d) 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
${(\Delta Q)_{{\rm{isobaric}}}} = {(\Delta Q)_{{\rm{isochoric}}}}$==> $\mu \,{C_p}{(\Delta T)_A} = \mu \,{C_v}{(\Delta T)_B}$
==>${(\Delta T)_B} = \frac{{{C_p}}}{{{C_v}}}{(\Delta T)_A} = \gamma {(\Delta T)_A} = 1.4 \times 30 = 42\,K.$
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