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. 21 K
B. 35 K
C. 42 K
D. 70 K

Answer

C

Explanation

For cylinder A :
From first law of thermodynamics,
`Q = DeltaU + W`
Process 'A' is a constant pressure process `(DeltaU = 0)`
` W = (muR)/(gamma-1)(T_(2)-T_(1))`
`implies W = (1 xx R)/(((5)/(3)-1)) xx (42)` ` (because mu = 1, gamma = (5)/(3))`
`therefore W = 63 R`
` therefore Q = 63 R`
Process 'A' is a constant volume process
`W = 0`
`Q = muC_(V)Delta T`
`implies Q = = 1 xx (3)/(2) R xx Delta T` `( because C_(V) = (3)/(2) R)`
`therefore Q = (3)/(2)R Delta T` ...( 2)
As the heat supplied to both cylinders is same
`63 R = (3)/(2)R Delta T`
`Delta T = 42 K `