A vessel of volume V contains an ideal gas at absolute temperature T a

Question - A vessel of volume

V

contains an ideal gas at 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 the gas that have leaked is

Options:

A . VRT(P + P′)

B . V2RT(P + P′)

C . VRT(P − P′)

D . V2RT(P − P′)

Answer: Option C
:
C
Number of moles present initially is

n = \frac{P V}{R T}

. Let

n^{'}

be the number of moles of the gas that leaked till
the pressure falls to

P^{'}

. Since volume V of the vessel cannot change and temperature T remains
constant during leakage, we have

n^{'} = \frac{P^{'} V}{R T}

∴

Number of moles that leaked is

Δ n = n - n^{'} = \frac{P V}{R T} - \frac{P^{'} V}{R T} = \frac{V}{R T} (P - P^{'})

So the correct choice is (C)

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