`A` vertical cylinder of cross-section area `A` contains one mole of an ideal mono-atmic gas under a piston of mass `M` At a certain instant a heater which supplies heat at the rate q `J//s` is switched `ON` under the piston. The velocity with which the piston moves upward under the condition that pressure of gas remains constant is [Assume on heat transfer through walls of cylinder]

Options

A. constant and equal to `(2)/(5)xx(q)/(p_(0)A+Mg)`
B. constant and equal to `(3)/(5)xx(q)/(p_(0)A+Mg)`
C. varying
D. constant but can't be determined from given information.

Answer

A

Explanation

From equilibrium of piston, `pA=p_(0)A+Mg` where `P` is presseure of gas.
From first law of thermodynamics `Q=DeltaU+W`
`int nC_(p)dT=intnC_(v)dT+intpdV`
`nC_(p)DeltaT=nC_(v)DeltaT+intpAdx`
`nxx(5R)/(2)DeltaT-nxx(3)/(2)RDeltaT=intpAdx`
`int pAdx=1xxRDeltaT Also Q=int qdt`
So, `int pAdx=int q dt-(3)/(2)RDeltaTimpliesq dt=(5)/(2) pAdx`
`implies(dx)/(dt)=(2)/(5)xx(q)/(pA)=(2)/(5)xx(q)/(p_(0)A+Mg)`