an ideal gas is enclosed in a container of volume v at a pressure p. it is being pumped out of the container by using a pump with stroke volume v. what is the final pressure in container after n stroke of the pump?
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Initial pressure = P Volume = V Let the initial temperature be T
P V = n R T
stroke volume of the pump = v (let v << V)
Assuming an isothermal process:
After the pumping out gas of volume v out of V, the number of moles of the given gas left in the container = n *(V-v)/V
As Volume V of the container is constant,
P1 = P * (V-v)/V = P (1 - v/V)
Again when gas is pumped out pressure will become
P2 = P1 * (1 - v/V) = P (1- v/V)²
After n pumpings, Pressure inside the container = P (1 - v/V)ⁿ
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P V = n R T
stroke volume of the pump = v (let v << V)
Assuming an isothermal process:
After the pumping out gas of volume v out of V, the number of moles of the given gas left in the container = n *(V-v)/V
As Volume V of the container is constant,
P1 = P * (V-v)/V = P (1 - v/V)
Again when gas is pumped out pressure will become
P2 = P1 * (1 - v/V) = P (1- v/V)²
After n pumpings, Pressure inside the container = P (1 - v/V)ⁿ
====
kvnmurty:
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