Two cylinders of equal size are filled with equal amount of ideal diatomic gas at room temperature. Both the cylinders are fitted with pistons. In cylinder A the piston is free to move, while in cylinder B the piston is fixed. When same amount of heat is added to both the cylinders, the temperature of the gas in cylinder A raises by 20 K. What will be the rise in temperature of the gas in cylinder B?

Options

A. `42^@K`
B. `30^@K`
C. `20^@K`
D. `56^@K`

Answer

A

Explanation

Since, cylinder A undergoes isobaric and cylinder B isochoric process
`Q_A= nC_P DeltaT, Q_B=nC_v DeltaT.`
As `Q_A= Q_B`
`implies nC_p DeltaT=nC_v DeltaT.`
`implies Delta T. = (C_p)/(C_v) xx DeltaT=7/5 xx 30 =42 K`.