`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 whise 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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Options

A. `(k)/(50R)`
B. `(k)/(100R)`
C. `(k)/(110R)`
D. `(k)/(90R)`

Answer

B

Explanation

`(DeltaQ)/(Deltat) = (Deltaw)/(Deltat)` work done per unit time `= (ka theta)/(L)`
`"Power" = F xx "Velocity" = PAV' = (nRT)/(v) AV`
where `V rarr` volume `V' rarr` velocity
`rArr (0.5 R(300))/(V) AV' = (ka theta)/(L)`
`(0.5 R(300))/(A (L)/(2))AV' = (ka theta)/(L) rArr V' = (ka)/(R) ((27)/(300)) = (k)/(100R)` .