Two cylinder A and B fitted with pistons contain equal number of moles of an ideal monoatomic gas at 400 K . The piston of A is free to move while that of B is held fixed . Same amount of heat energy is given to the gas in each cylinder . If the rise in temperature of the gas in A is 42 K, the rise in temperature of the gas in B is

Options

A. 25.2 K
B. 35 K
C. 42 K
D. 70 K

Answer

A

Explanation

Case (i): Piston is fixed
`DeltaQ = DeltaU + DeltaW`
`DeltaQ = n xx (3R)/(2)xx 42 + 0` `(because Volume - Constant)`
Case (ii): piston is free to move
`DeltaQ = nCp dT`
`n xx (3R)/(2) xx 42 = n xx (5R)/(2) xx dT`
`dT = (3xx42xx2)/(2xx5)`
`dT = 25.2 K`