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

d. For `A:` As piston is free to move, the process is isobaric.
`Delta Q = mu C_(v) (Delta T)_(1)`
For `B` : As piston is held fixed, the process is isochoric
`:. Delta Q = mu C_(v) (Delta T)_(2)`
Now `C_(P) (Delta T)_(1) = C_(V) (Delta T)_(2)`
`(7R)/(2) xx 30 = (5 R)/(2) (Delta T)_(2)`
`:. Delta T_(2) = 42 K`