where P is the total pressure of the system, and Psat(Ta) is the saturation pressure of the
vapor evaluated at the air temperature Ta. The small change in system pressure is not
accounted for in evaluating the properties. The definition of the mass transfer coefficient
is applied to the differential control volume to obtain the following,
(mV,,,,) = kGa pf,~sat (7L) T',rrT ())A, (3.4)
where kG; is the gas mass transfer coefficient, aw is the wetted specific area, and A is the
cross sectional area of the diffusion tower. It should be noted that the total specific area
of the packing, a, is the total surface area of packing per unit volume of space occupied.
The rate of change of evaporation can be further reduced by considering the perfect gas
law. By applying the perfect gas law [18] to Equation 3.4, the rate of evaporation
becomes,
(mVevap) = kG w A, T (3.5)
where My is the molecular weight of vapor, R is the universal gas constant, and Ti is the
liquid/vapor interfacial temperature. By combining Equations 3.2-3.5 the gradient of the
humidity ratio is,
de kG~ 2T M ,, E,(7) P
dz G R 7 0.622 +0 (i ; 3
where G = 0I is the air mass flux. Equation 3.6 is a first order ordinary differential
equation with dependent variable co. When solved, the humidity ratio along the axial z
direction is obtained. Equation 3.6 requires a value of the liquid/vapor interfacial