## Vapour Pressure And Evaporation

The concept of vapour pressure is needed in order to explain why a liquid is sometimes depleted by evaporation and sometimes augmented by condensation. We first consider gas molecules in a box, which move to and fro, continually colliding with each other and with the walls of the box. Everything is at the same temperature. (Such a model of colliding molecules is the basis of the Kinetic Theory of Gases outlined by Rudolf Clausius in 1857.) The molecules' impacts press the walls outwards, with a total pressure partly due to the molecules of water vapour. That part is called the 'water-vapour pressure', or, simply, 'vapour pressure'. The rest of the total pressure is exerted by the other molecules of air inside the box, e.g. the molecules of nitrogen and oxygen.

### Saturation

If both water vapour and liquid are contained in the same box (Figure 4.3), we can show that adjustments occur towards an eventual steady balance, when the amount of evaporation from the liquid equals the condensation back from the vapour. The reasoning is as follows. The temperature governs the rate at which evaporation occurs, because it controls the liveliness of the liquid's molecules and hence their readiness to escape their bonds. Then, as individual molecules enter the space above, they add to the number of vapour molecules, which increases the frequency of bombardment of all the adjacent surfaces, one of which is that of the liquid itself. As a consequence of there being more vapour molecules, more of them hit the liquid's surface and condense, becoming re-imprisoned in the liquid. Eventually, sufficient evaporation into the space has occurred for there to be enough vapour to return molecules to the liquid at an equal rate, i.e. the condensation rate matches the evaporation rate. At that stage, the space above the liquid is said to be saturated, and the pressure exerted by the vapour in it is the saturation vapour pressure, (svp) represented by e.. Strictly speaking, this vapour Figure 4.2 An example of latent-heat transfer.

ff A

ff A Figure 4.3 The principle of equilibrium between water and vapour in an enclosure. Molecules C impact on each surface with a vigour depending on their temperature, and thus create vapour pressure. Molecules A escape from the liquid, according to the liquid's temperature. On the other hand, molecules B impact on the liquid and are recaptured, according to the number of molecules in the space above the liquid. When steady conditions are reached, the numbers of kinds A and B are equal.

Figure 4.3 The principle of equilibrium between water and vapour in an enclosure. Molecules C impact on each surface with a vigour depending on their temperature, and thus create vapour pressure. Molecules A escape from the liquid, according to the liquid's temperature. On the other hand, molecules B impact on the liquid and are recaptured, according to the number of molecules in the space above the liquid. When steady conditions are reached, the numbers of kinds A and B are equal.

pressure applies only to the water vapour in the saturated space (i.e. to a gas), but since it is in balance with that from the liquid we can regard es as applying to the liquid too.

The result is that es depends only on the temperature, since this alone determines the rate of evaporation, and therefore the amount of vapour needed to provide an equal rate of condensation. This is one of the most basic facts about the atmosphere, and must be grasped to make sense of Chapters 6-8. The increase of es with temperature is shown in what is called the psychrometric table (Table 4.1), determined by laboratory measurements in the context of theoretical work by Clausius. The relationship between es and temperature is discussed further in Chapter 6.

In practice, equilibrium between evaporation and condensation is rarely achieved in the real world. Usually one of the processes is dominant since adjacent air and water tend to be at different temperatures, and to have different vapour pressures. So there is a net difference between the flow from the place at higher vapour pressure and the smaller flow from the place at lower pressure. In fact, the (net) evaporation rate from water is proportional to the vapour-pressure difference (es-e), where e is the local atmosphere's vapour pressure (or ambient vapour pressure) and es is the liquid's vapour pressure, i.e. the saturated vapour pressure (e) at the liquid's surface temperature (Note 4.C).