The vapour pressure of steam in moist air

It is worth pausing a moment to consider the validity of the ideal gas laws as they are applied to the mixture of gases which comprises moist air.

Kinetic theory, which supports the ideal gas laws, fails to take account of the fact that intermolecular forces of attraction exist. In a mixture such forces occur between both like molecules and unlike molecules. That is to say, between molecules of dry air, between molecules of steam and between molecules of steam and dry air. The virial coefficients mentioned in section 2.4 attempt to deal with the source of error resulting from attractive forces between like molecules. To offset the error accruing from the forces between unlike molecules, a further set of ‘interaction coefficients’ (sometimes termed ‘cross-virial’ coefficients) is adopted.

An explanation of the modern basis of psychrometry, taking these forces into account, is

Given in section 2.19. For the moment, and for most practical purposes, we can take it that the saturation vapour pressure in humid air depends on temperature alone; that is, it is uninfluenced by barometric pressure.

EXAMPLE 2.3

Determine the saturation vapour pressure of moist air (a), at 15°C and a barometric pressure of 101325 Pa and (b) at 15°C and a barometric pressure of 95 000 Pa.

Answer

(a) From CIBSE tables of psychrometric data, at 15°C dry-bulb and 100 per cent saturation, the saturation vapour pressure is 1704 Pa.

(b) From the same source exactly, we determine that the saturation vapour pressure is 1704 Pa at 15°C dry-bulb and 100 per cent relative humidity. We can, of course, use the CIBSE tables of psychrometric data for determining this saturation vapour pressure, even though the question speaks of 95 000 Pa, since saturation vapour pressure does not depend on barometric pressure. On the other hand, it should be noted that at all relative humidities less than 100 per cent the vapour pressures quoted in these tables are valid only for the total or barometric pressure for which the tables are published, namely, 101 325 Pa.

To illustrate the distinction between saturated vapour pressure and superheated vapour pressure, consider a sample of liquid water within a closed vessel. On the application of heat evaporation occurs, and for every temperature through which the liquid passes there is an equilibrium pressure, as has already been discussed. Figure 2.5(a) shows a curve A, B, B’ representing the relationship between saturation vapour pressure and absolute temperature. If heat is applied to the vessel beyond the instant when the last of the liquid water turns to saturated steam, the change of state of the steam can no longer be represented by the curve. The point B represents the state of the contents of the vessel at the instant when the last of the liquid has just evaporated. The vessel contains dry saturated steam but, unlike the case so far, no liquid is present. By our earlier assumptions then, the contents of the vessel approximate an ideal gas and, therefore, may be taken to obey Charles’ law for any further heating at constant volume. Equation (2.6) states this law, and further changes of state of the steam in the closed vessel may be represented by a straight line. This is shown in Figure 2.5(a) by the line BC.

The changes can also be shown on another sort of diagram, Figure 2.5(b), where pressure and volume are used as co-ordinates. The total volume of the liquid and vapour has remained constant throughout the application of all the heat, hence changes on the p — V diagram must occur along a line of constant volume, for this example. At condition A the vessel contains saturated liquid and saturated vapour. Accordingly, on the p — V diagram state A must lie within the wet zone. On the other hand, at point B the contents of the vessel are saturated steam only, hence B lies on the saturated vapour line. It can be seen that the change of state into the superheated zone at C is an extension of the vertical line AB as far as C.

It is seen later (sections 2.10 and 2.19) that, for a mixture of steam and dry air, there is a relationship between the mass of steam in the mixture and the vapour pressure it exerts. Since the thermodynamic properties of saturated steam and dry air are well established, it is possible, according to Goff (1949), to express the vapour pressure of the steam present in a mixture on a proportional basis, related to the mass of steam present in the mixture. Thus, for 1 kg of dry air only, the vapour pressure is zero but, for a mixture of saturated

Steam and 1 kg of dry air, the vapour pressure is given by equation (2.10) or (2.11). For a lesser amount of steam mixed with 1 kg of dry air, the vapour pressure exerted by the steam present would be between zero and the saturated pressure, in proportion to the mass of water vapour in the mixture. This leads to the concept of percentage saturation and is dealt with in section 2.11.

It is to be noted that, when steam is mixed with dry air but the steam is not saturated, it

Is in the superheated state. For example, such steam would be represented by the point C in Figure 2.5(b) rather than by the point B.

Posted in Engineering Fifth Edition