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Q.

A thermally insulated vertical cylinder of cross section area A contains 3 moles of an ideal monoatomic gas under a piston of mass M. A heater supplying heat to the gas at constant rate PJ/s, is switched on at t=0. The velocity of the piston is given by [Take atmosphere pressure as p₀]

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a

$\frac{2 P}{5 [p_{0} A + Mg]}$

b

$\frac{3 P}{5 [p_{0} A + Mg]}$

c

$\frac{3 P}{2 [p_{0} A + Mg]}$

d

$\frac{P}{[p_{0} A + Mg]}$

answer is A.

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Detailed Solution

$\begin{array}{l} \frac{dω}{dQ} = \frac{dQ - dU}{dQ} = 1 - \frac{dU}{dQ} = 1 - \frac{1}{γ} = 1 - \frac{3}{5} = \frac{2}{5} \\ dω = \frac{2}{5} dQ; \frac{2}{5} pdt = Fds \\ \frac{2}{5} P = (P_{0} A + mg) \frac{ds}{dt} \\ ∴ v = \frac{2}{5} \frac{p}{(p_{0} A + mg)} \end{array}$

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