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

In cylinder A heat is supplied at constant pressure while in cylinder B heat is supplied at constant volume.
`therefore" " (DeltaQ)_(A)=nCp(DeltaT)_(A)` …(i)
`"and" " " (DeltaQ)_(B)=nCv(DeltaT)_(B)` …(ii)
`"Given"" " (DeltaQ)_(A)=(DeltaQ)_(B)`
`therefore" " (DeltaT)_(B)=(C_(p))/(C_(v))(DeltaT)_(A)=1.4xx30(therefor(C_(p))/(C_(v))=(1)/(4))`
`(DeltaT)_(B)=42K`