BITSAT 2015 Paper

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 mass less piston.

The cylinder is attached with a conducting rod of length L , cross-section area (1/9) m2 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 velocity of piston when it is at height L/2 from the bottom of cylinder is :
[Neglect any kind of heat loss from system ]