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%