`A` vertical cylinder pistion system has cross-section `S`. It contains `1` mole of an ideal monoatomic gas under a pistion of mass `M`.At a certain instant a heater is switched on which transmits a heat `Q` per unit constant and the system is thermally insulated.

Explanation

Gas pressure =`P_(0)+(Mg)/(S)`,Where M is mass of the pistion.
As `C_(v)=(3)/(2)R`
`therefore` `triangleU =(3)/(2)RtriangleT=(3)/(2)PtriangleV`
`Q=PtriangleV+triangleU==PtriangleV=(5)/(2)PtriangleV`
`triangleV=Sdx`
or `Q=q.dt=(5)/(2)PSdx`
or `(dx)/(dt)=(2q)/(5PS)=(2q)/(5(P_0+(Mg)/(S))S`