Two cylinders `A` and `B` fitted with pistons contain equal amounts of 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

Options

A. `30K`
B. `18K`
C. `50K`
D. `42K`

Answer

D

Explanation

A is free to move, therefore, heat will be supplied at constant pressure.
`dQ_(A)=nC_(p)dT_(A)` (i)
`B` is held fixed, therefore, heat will be supplied at constant volume.
`dQ_(B)=nC_(V)dT_(B)` (ii)
But `dQ_(A)dQ_(B)`
`nC_(p)dT_(A)=nC_(V)dT_(B)`
`dT_(B)=((C_(p))/(C_(V)))dT_(A)`
`=gamma(dT_(A))`
`[gamma=1.4("diatomaic")]`
`(dT_(A)=30K)`
`=(1.4)(30K)`
`dT_(B)=42K`