Two moles of a diatomic gas at `300K` are enclosed in a cylinder as shown in figure. Piston is light. Find out the heat given if the gas is slowly heated to `400K` in the following three cases.
(i) Piston to free to move
(ii) If piston does not move
(iii) If piston is heavy and movable

Explanation

(i) Since pressure is constant
`:. DeltaQ = nC_(P)DeltaT = 2 xx (7)/(2) xx R xx (400 - 300) = 700R`
(ii) Since volume is constant
`:. W = 0`and `DeltaQ = DeltaU` (from first law)
`DeltaQ = DeltaU = nC_(v)DeltaT = 2 xx (5)/(2) xx R xx (400-300) = 500R`
(iii) Since pressure is constant
`:. DeltaQ = nC_(P)DeltaT = 2 xx (7)/(2) xx R xx (400 -300) = 700R`