Heat And Thermodynamics

0.5 mole of an ideal gas at constant temperature \(27^{\circ} \mathrm{C}\) kept inside a cylinder of length \(L\) and cross-section \(A\) closed by a massless piston. The cylinder is attached with a conducting rod of length L\(_1\) cross-section area \((1 / 9) \mathrm{m}^2\) and thermal conductivity \(k_1\) whose other end is maintained at \(0^{\circ} \mathrm{C}\). If piston is moved such that rate of heat flow through the conduction 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)