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
`therefore Delta Q = n C _(p) Delta T =2 xx 7/2 xx R xx (400 -300) =700 R`
(ii) Since volume is constant
`therefore Delta W =0 and Delta Q = Delta u` (from first law)
`Delta Q = Delta u = n C _(v) Delta T =2 xx 5/2 xx R xx (400-300)=500R`
(iii) Since pressure is constant
`therefore Delta Q =n C _(P) Detla T =2 xx 7/2 xx R xx (4000 -300)=700R`