# The specific heat capacity of humid air

The air supplied to a conditioned room in order to remove sensible heat gains occurring therein, is a mixture of dry air and superheated steam (see chapter 2). It follows that these two gases, being always at the same temperature because of the intimacy of their mixture, will rise together in temperature as both offset the sensible heat gain. They will, however, offset differing amounts of sensible heat because, firstly, their masses are different, and secondly, their specific heats are different too.

Consider 1 kg of dry air with an associated moisture content of g kg of superheated steam, supplied at temperature ts in order to maintain temperature tx in a room in the presence of sensible heat gains of Q kW. A heat balance equation can be written thus:

Q = 1 x 1.012 x (tT — ts) + gx 1.890 x (tT — ts)

Where 1.012 and 1.890 are the specific heats at constant pressure of dry air and steam respectively. Rearrange the equation:

Q = (1.012 + 1.89*)(fr-fs)

The expression (1.012 + 1.89g) is sometimes called the specific heat of humid air.

Taking into account the small sensible cooling or heating capacity of the superheated steam present in the supply air (or its moisture content) provides a slightly more accurate answer to certain types of problem. Such extra accuracy may not be warranted in most practical cases but it is worthy of consideration as an exercise in fundamental principles.

EXAMPLE 6.5

Calculate accurately the weight of dry air that must be supplied to the room mentioned in example 6.4, given that its associated moisture content is 7.500 g kg-1 of dry air and that the specific heat at constant pressure of superheated steam is 1.890 kJ kg-1 K-1.

124 The choice of supply design conditions Answer

By equation (6.5)

2 = m x (1.012 + 0.0075 x 1.89) x (22 — 13) m = 2/(1.026 x 9) = 0.2166 kg dry air per second

This should be compared with 0.2196 kg s’1 the answer to example 6.4(a). Note that, for the moisture content quoted, the specific heat of the humid air is 1.026 kJ kg-1 K-1.

Posted in Engineering Fifth Edition