Page:Journal of the American Society of Mechanical Engineers, Volume 33.pdf/681



86Assuming 1 lb. of pure air having the temperature $$t$$ containing $$W$$ lb. of moisture with the corresponding dew point hand vapor pressure $$e_1$$ having a resultant adiabatic saturation temperature of $$t'$$, assume also a moisture increment $$dW$$ under adiabatic conditions resulting in a temperature increment of $$-dt$$. This moisture increment $$dW$$ is evidently evaporated at a vapor pressure $$e_1$$ corresponding to temperature $$t_1$$ and superheated to temperature $$t$$. The temperature of the liquid is evidently constant at temperature $$t'$$, from principle C. The total heat of the vapor in the increment is $$H_1 dW + C_{ps} (1 - t_1) dW$$, where $$H_1$$ is the total heat of steam corresponding to temperature $$t_1$$ and vapor pressure $$e_l$$, and $$C_{ps} (t - t_1) dW$$ is the heat required to superheat from saturation temperature $$t_1$$ to dry-bulb temperature $$t$$. The heat of the liquid evaporated, however, is $$q' dW$$ corresponding to temperature of saturation $$t'$$.

87 The total heat interchange required to evaporate $$dW$$ under these conditions is therefore

The change in sensible heat of 1 lb. of air and $$W$$ lb. of water vapor due to the temperature increment $$-dt$$ is

Since the change is adiabatic these values may be related by the equation

in which $$H_1$$ and t_1 are variables corresponding to the variable $$W$$ while $$t$$ is a variable related to $$W$$ by the different equation. A constant corresponding to $$t'$$ is $$q'$$ while $$C_{ps}$$, may be taken approximately as a mean between its values at $$t_1$$ and at $$t'$$ and $$C_{ps}$$ as a mean between its values at $$t$$ and at $$t'$$. The temperature of saturation is $$t'$$, and $$W'$$ is the corresponding moisture content at saturation.

88It is not necessary, however, to solve this equation in this form as this relationship may be simpliﬁed.