A small amount of water and its saturated vapour are enclosed in a vessel at a temperature $$t = 100^0C$$. How much (in per cent) will the mass of the saturated vapour increase if the temperature of the system goes up by $$\Delta T = 1.5 \ K$$? Assume that the vapour is an ideal gas and the specific volume of water is negligible as compared to that of vapour.
From $$C-C$$ equation, neglecting the volume of the liquid
$$\dfrac{dp}{dT} = \dfrac{q_{12}}{TV'_2} = \dfrac{Mq}{RT^2}p, (q = q_{12})$$
or $$ \dfrac{dp}{p} = \dfrac{Mq}{RT} \dfrac{dT}{T}$$
Now $$pV= \dfrac{m}{M} RT or m = \dfrac{MpV}{RT}$$ for a perfect gas
So $$\dfrac{dm}{m} = \dfrac{dp}{p} - \dfrac{dT}{T}$$ (V is Const = specific volume)
$$\dfrac{dm}{m}= \Big( \dfrac{Mq}{RT} - 1 \Big) \dfrac{dT}{T} = \Big( \dfrac{18 \times 2250}{8.3 \times 373} - 1 \Big) \times \dfrac{1.5}{373} = 4.85 \%$$