Q:A gas is enclosed in a vessel at a constant temperature at a pressure of 2.5 atmospheres and a volume of 4 litres. Due to a leak in the vessel, after some time the pressure is reduced to 2 atmospheres. As a result :

(a) 20% of the gas remains in the vessel

(b) 20% of the gas escapes out

(c) 25% of the gas escapes out

(d) 25% of the gas remains in the vessel.

Ans:(b)

Sol: PV = constant.

Differentiating it we get

P dV + V dP = 0

or, $ \displaystyle \frac{dP}{P} = -\frac{dV}{V} $

% of gas escaped is

$ \displaystyle -\frac{dV}{V}\times 100 = \frac{dP}{P} \times 100 $

$ \displaystyle = \frac{2.5-2}{2.5}\times 100 $

= 20%