First slide

laws

Question

A vessel of volume V contains an ideal gas absolute temperature T and pressure P. The gas is allowed to leak till its pressure falls to P'. Assuming that the temperature remains constant during leakage, the number of moles of gas that have leaked is

Easy

A

$\frac{V}{RT} (P + P')$
B

$\frac{V}{2 RT} (P + P')$
C

$\frac{V}{RT} (P - P')$
D

$\frac{V}{2 RT} (P - P')$

Solution

V = constant ; T = constant ; We know that
$PV = μRT \Rightarrow μ_{1} = \frac{PV}{RT}$
After leakage,
$P' V = μ_{2} RT μ_{2} = \frac{P' V}{RT}$
Therefore the number moles of the gas that have leaked is
$μ_{1} - μ_{2} = \frac{PV}{RT} - \frac{P' V}{RT} = \frac{V}{RT} (P - P')$

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