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.

Two moles of an ideal monoatomic gas are contained in a vertical cylin

1.	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» Correct Answer - `(2q)/(5(mg+P_(0)A))` `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))`.

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