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Question

A vessel of volume V0 contains an ideal gas at pressure P0 and temperature T. Gas is continuously pumped out of this vessel at a constant volume -rate dV/dt=r keeping the temperature constant. The pressure inside the vessel. Find (a) The pressure of the gas as a function of time, (b) the time is taken before half the origin gas is pumped out.

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Solution

dVdt=rdV=r dt
Let the pumped out gas pressure dp
Volume of container =V0 At a pump dv amount of gas has been pumped out.
Pdv=V0dfPvdf=V0dp
PPdpp=10dtrV0P=Pert/V0
Half of the gas has been pump out, Pressure will be half =12evt/V0
ln2=rtV0
t=ln2γ0r

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