Two moles of an ideal monoatomic gas are contained in a vertical cylinder of cross sectional area `A` as shown in the figure. The piston is frictionless and has a mass m. At a certain instant a heater starts supplying heat to the gas at a constant rate `q J//s`. Find the steady velocity of the piston under isobaric condition. All the boundaries are thermally insulated.

Answer

`(2q)/(5(mg+P_(0)A))`

Explanation

`dQ_(p) = nC_(p)dT`
Let heat be supplied for time dt
`:. qdt =2. (5R)/(2). ([(mg)/(A)+P_(0)]Adx)/(2R)`
where `[dT = (Pdv)/(nR)]`
`:. qdt = (5)/(2) (mg +P_(0)A) dx`
`:. (dx)/(dt) = (2q)/(5(mg+P_(0)A))`.