Two cylinders A and B fitted with piston contain equal amount of an ideal diatomic as at temperature ' $T$ '…
Two cylinders A and B fitted with piston contain equal amount of an ideal diatomic as at temperature ' $T$ ' K . The piston of cylinder 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 temperature of the gas in A is ' $\mathrm{dT}_{\mathrm{A}}$ ', then the rise in temperature of the gas in cylinder B is $\left(\gamma=\frac{\dot{\mathrm{C}}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}\right)$
$\quad 2 \mathrm{dT}_{\mathrm{A}}$
$\frac{\mathrm{dT}_{\mathrm{A}}}{2}$
$\gamma \mathrm{dT}_{\mathrm{A}}$
$\frac{\mathrm{dT}_{\mathrm{A}}}{\gamma}$
Solution
In cylinder A , heat is supplied at constant pressure while in B at constant volume
$\begin{aligned}
& \mathrm{Q}_{\mathrm{A}}=\mathrm{Q}_{\mathrm{B}} \\
& \mathrm{nC}_{\mathrm{p}} \mathrm{dT}_{\mathrm{A}}=\mathrm{nC}_{\mathrm{v}} \mathrm{dT}_{\mathrm{B}} \\
& \mathrm{dT}_{\mathrm{B}}=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}} \mathrm{dT}_{\mathrm{A}}=\gamma \mathrm{dT}_{\mathrm{A}}
\end{aligned}$