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:

in first case heat is supplied at constant pressure 

$\therefore {\text{Q}}_A{\text{=nC}}_{\text{p}}{\text{ΔT}}_{\text{1}}$

And in second case heat is supplied at constant volume

$\therefore {\text{Q}}_B{\text{=nC}}_v{\text{ΔT}}_2$

here n = number of moles of gas

$C_P$ = specific heat of gas at constant pressure 

$C_v$=specific heat of gas at constant volume 

$∆T$=change in temperature

$\begin{array}{rcl}{Q}_B& =& Q_A as amount of heat given is same\\ {\text{nC}}_v{\text{ΔT}}_2& =& {\text{nC}}_p{\text{ΔT}}_1\end{array}$

For ${\text{ΔT}}_2=\frac{{\text{C}}_{\rho }}{{\text{C}}_v}.{\text{ΔT}}_1$

substitute specific heat ratio for diatomic gas =7/5

${\text{ΔT}}_2=\frac{7}{5}.30=42\text{\hspace{0.17em}K}$=rise in temperature of gas in B