A vessel of volume v0 contains an ideal gas

Asked by admin @ 23/08/2021 in Physics viewed by 315 People

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 of the gas being taken out equals the pressure inside the vessel. Find (a) the pressure of the gas as a function of time, (b) the time taken before half the original gas is pumped out.

Answered by admin @ 23/08/2021

In 2 = rt/Vo

t = In^2ro/r

Explanation:

dV/ dt = r

It implies dV = r

Let the pumped out gas pressure be dp.

Volume of container = V0

At a pump, dv amount of gas has been pumped out.

Pdv = –V0df

Pv df = –V0 dp

Differential applied on both sides, we get:

Differential of P to P of dp/p = differential of 0 to 5 of dtr/Vo

We get P = P e^-rt/Vo

Please refer the attached picture for corret formatting of the equation.

Half of the gas has been pumped out.

Pressure will be half = 1/2e^-vt/vo

In 2 = rt/Vo

t = In^2ro/r

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