Two cylinders fitted with pistons contain equal amount of an ideal diatomic gas at 300K. The 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 30K, then the rise in temperature of gas B is

Options

A. `30 K`
B. `18 K`
C. `50 K`
D. `43 K`

Answer

D

Explanation

A is free to move, therefore, heat will be supplied at constant pressure.
`dQ_A = nCpdT_A" ...(i)"`
B is held fixed, therefore, heat will be supplied at constant volume.
`dQ_B = n C_V dTB" ...(ii)`
But `dQ_A = d Q_B, " "nCpdT_a = n C_V dT_B`
`dT_B = (C_p/C_V)dT_A = gamma (dT_A)" "[gamma = (dV)/(VdT) = 3/T("diatomic")]`
`(d T_A = 30 K)" "=(1.4)(30 K)" "dT_B = 42 K`