Humid air


We consider humid air at the temperature of 20^\circ C and pressure 1~bar. Humidity expressed with the mixing ratio is x=0.014. Estimate absolute humidity \rho_w, relative humidity \phi, mass fraction of water vapour \xi_w and molar fraction of water vapour \psi_w in air!




Mass fraction (mass of water vapour / mass of humid air) is connected to mixing ratio (mass of water vapour / mass of dry air) by


Humid air is a mixture of air and water vapour, so the mass fraction of air is \xi_z=1-\xi_v=0.9862. Since mass fractions are now know, we can estimate the molar fraction of water vapur as

    \[\psi_v=\frac{\xi_w/ M_w}{\sum_j\xi_j/M_j}=\frac{\xi_w/ M_w}{\xi_w/M_w+\xi_a/M_a}=0.022,\]

where M_w and M_a are the molar masses of water and air, respectively. Molar fraction can be used to estimate partial pressure of water vapour:


Using an engineering handbook we find that the saturated partial pressure of water vapour at temperature 20^\circ C and pressure 1~bar is p_{w,s}=2337~Pa. Using this, we calculate the relative humidity as


Finally, absolute humidity (i.e. the mass concentration of water vapour in the air) is calculated by assumig that air is an ideal gas


Here R=8314~J/(kmolK).

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