X and Y are two cylinders, fitted with frictionless pistons. Both of them contain equal amounts of oxygen at 200K. Equal amount of heat is given to the gas in each cylinder. However, the piston of A is fixed while that of B is movable. What is the rise in temperature of the gas in B, if the rise in temperature of A is 42 K ?

Options

A. 50 K
B. 40 K
C. 30 K
D. 25 K

Answer

C

Explanation

The piston of A is fixed. Hence the gas in it is heated at constant volume.
`therefore` Heat absorbed by `O_(2)` in A is `Q_(1)=nC_(V)(dT_(1))`
and since the piston of B is movable, the gas in B is heated at constant pressure (atmospheric pressure) and the heat absorbed by oxygen in B is `Q_(2)=nC_(P)(dT_(2))`
For a diatomic gas like `O_(2),C_(V)=5/2RandC_(P)=7/2R`
and since `Q_(1)=Q_(2)anddT_(1)=42`
`thereforenC_(V)(dT_(1))=nC_(P)(dT_(2))`
`therefore5/2Rxx42=7/2R(dT_(2))`
`therefore7(dT_(2))=210" "therefore(dT_(2))=30K`
`therefore` Rise in temperature of the gas in B = 30 K