Question

A gas is contained in a vessel of volume vo at a pressure po. if the gas is to be pumped out by a suction pump of stroke volume v them the number of moles of gas remained in the vessel after two stroke is
1.povo^3/rt(vo+v)^2
2.povo^2/rt(vo+v)^2
3.povo^3/rt(vo+v)^3
4.povo^2/rt(vo+v)^3

Answer 1

Given that,

Initial volume = V₀

Initial pressure = P₀

Stroke volume = V

We know that,

The equation of ideal gas

$PV=nRT$

Where, P = pressure

V = volume

R = gas constant

T = temperature

If T remains constant, then after a stroke of pump

$PV=P_{1}V_{1}$

So, after first stroke of pump,

We need to calculate the pressure after first stroke

Using formula for pressure

$P_{0}V_{0}=P_{1}(V_{0}+V)$

$P_{1}=\dfrac{P_{0}V_{0}}{(V_{0}+V)}$....(I)

We need to calculate the pressure after second stroke

Using formula for pressure

$P_{1}V_{0}=P_{2}(V_{0}+V)$

$P_{2}=\dfrac{P_{1}V_{0}}{(V_{0}+V)}$

Put the value of P₁

$P_{2}=\dfrac{\dfrac{P_{0}V_{0}}{(V_{0}+V)}V_{0}}{(V_{0}+V)}$

$P_{2}=\dfrac{P_{0}V_{0}^2}{(V_{0}+V)^2}$

We need to calculate the number of moles of gas after two stroke

Using formula of pressure after second stroke

$P_{2}V_{0}=nRT$

$n=\dfrac{P_{2}V_{0}}{RT}$

Put the value of P₂

$n=\dfrac{P_{0}V_{0}^2}{(V_{0}+V)^2}\times\dfrac{V_{0}}{RT}$

$n=\dfrac{P_{0}V_{0}^3}{RT(V_{0}+V)^2}$

Hence, The number of moles of gas after two stroke is $\dfrac{P_{0}V_{0}^3}{RT(V_{0}+V)^2}$

(1) is correct option.