Question

0.5 moles 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 (19)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 L2 from the bottom of cylinder is:[Neglect any kind of heat loss from system]

A
(kR)m/sec
B
(k10R)m/sec
C
(k100R)m/sec
D
(k1000R)m/sec
Solution
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△Q△t=△W△t= work done per unit time =kaθLdWdt=Pdvdt=kaθL,P=nRTV⇒0.5R(300VA.dldt=kaθL⇒0.5R(300)A.L2A.v=kaθL⇒v=kaR(27300)=k100R.

1
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