`0.5` mole of an ideal gas at constant temperature `27^(@)C` kept inside a cylinder of length `L` and cross-section area A closed by a massless piston The cylinder is attached with a conducting rod of length `L` cross-section area `(1//9)m^(2)` and thermal conductivity k whose other end is maintained at `0^(@)C` If piston is moved such that rate of heat flow through the conducing rod is constant then find velocity of piston when it is at height `L//2` from the bottom of cylinder [Neglect any kind of heat loss from system
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Answer

`0005`

Explanation

Temperature is constant Rightarrow `DeltaE =0 dW=nRT (dv)/v=nRT(Adx)/(AL//2)`
`Q=DeltaE+W`
Rightarrow`(dW)/(dt)=(nRT)/(L//2)(dx)/(dt)`
`(dQ)/(dt)=(dW)/(dt) Rightarrow 1/900 (DeltaT)/L=(2nRT)/L((dx)/(dt))`
`(dx)/(dt)=(kxx27)/(900.nRT)=(415.5xx27xx2)/(900xx0.5xx8.31xx300)=1/200 m//s = 5mm//s`