Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300K. The piston of A is free to move, while that 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 30K, then the rise in temperature of the gas in B is

Options

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

Answer

D

Explanation

For A : As piston is free to move, so process is isobaric
`DeltaQ = mu C_(p)(DeltaT)_(1)`
For B : As piston is held fixed, so process is isochoric
`:. DeltaQ = muC_(p)(DeltaT)_(2)`
Now, `C_(p)(DeltaT)_(1) = C_(V)(DeltaT)_(2)`
`(7R)/(2)xx30 = (5R)/(2) (DeltaT)_(2)`
:. DeltaT_(2) = 42K`.