Two cylinders Aand B fitted with pistons contain equal amounts of an ideal gas (diatomic) at 300 K. Thie 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. 30 K
B. 18 K
C. 50 K
D. 42 K

Explanation

The heat given to the gas in cylinder A is at constant pressure, while to that in cylinder B is at constant volume. If such cylinder contains the amount n of a diatomic gas, then
Heat give to the gas in cylinder `A = n C _(p,m ) Delta T = n((7)/( 2)R) (30 K )`
If this much heat is given to the cylinder B, then
`nC _( v,m) Delta T = n (( 7)/(2) R) (30 K) or n ((5)/(2) R) DeltaT = n ((7)/(2) R) (30K) or Delta T = (7)/(5) (30 K) = 42 K`