## Coexistence of the Three Phases of Water the Triple Point

The Clausius-Clapeyron equation may be applied to study the variation of saturated vapour pressure with temperature between any two phases of water, for example, between vapour (V) and liquid water (W), or between liquid and solid ice (I), or even directly between vapour and solid. For this purpose, we integrate Eq. (4.8.2) from the initial temperature 273.16A where the saturation vapour pressure is experimentally known to be 6.11 mb, to temperature T, by noting that the latent heat of a water substance does not vary appreciably within the ranges of temperature normally encountered in the atmosphere (see Eq. 4.8.3) during a change from one phase to the other. The resulting approximate expressions for the various changes of phase are the following:

(i) From vapour to liquid (condensation)

where L is the latent heat of condensation of water vapour(or vaporization of water). Its value at 273.16 A is 2.496 x 106 J kg-1.

(ii) From liquid to solid (fusion)

where Le is the latent heat of fusion of water(or melting of ice). Its value at 273.16A is 3.33 x 105Jkg-1.

(iii) From vapour to solid (sublimation)

where Lz is the latent heat of sublimation from vapour to solid (or solid to vapour). Its value at 273.16 A is 2.829 x 106 J kg-1.

Figure 4.4 is a phase diagram which shows the saturation vapour pressure, es, plotted against absolute temperature T for all the above-mentioned changes of phase. It shows that the curves representing the three phases meet at a point P which we call the triple point. At P, all the three phases co-exist

The curves separating the three phases are as follows: The curve AP representing the change from the liquid to the vapour phase extends from the triple point to

Fig. 4.4 Phase diagram in respect of water vapour - the Triple point

Figure 4.4 is a phase diagram which shows the saturation vapour pressure, es, plotted against absolute temperature T for all the above-mentioned changes of phase. It shows that the curves representing the three phases meet at a point P which we call the triple point. At P, all the three phases co-exist

The curves separating the three phases are as follows: The curve AP representing the change from the liquid to the vapour phase extends from the triple point to the critical point where the distinction between the liquid and vapour phases disappears. When the saturation vapour pressure equals the outside barometric pressure, water reaches its boiling point. The curve PB represents melting between water and ice. Since the specific volume of ice is greater than that of water, it follows from Eq. (4.8.1) that the melting line is negative and slightly curved. The curve PC which curves downward from P is the sublimation curve between the ice and the vapour phases. It may be noted that near P, the curvature of CP is greater than that of PA. This is due to the fact that the latent heat of sublimation of water vapour is greater than that of its condensation near the triple point. This follows fromEq. (4.8.1).

It is a fact of observation that water does not freeze immediately on cooling below 273.16A (or 0°C) temperature. It can stay in the supercooled liquid phase down to a temperature of about 233 A. However, the degree of freezing increases with lowering of temperature. The saturation vapour pressure over supercooled water is not given by the sublimation curve PC but by the dotted curve PQ in Fig. 4.4, which may be regarded as an extension of the curve AP to lower temperatures. An interesting aspect of the curve PQ is that the saturation vapour pressure over supercooled water is greater than that over ice at temperatures below 273.16A. This means that when supercooled water drops and ice crystals co-exist in the upper layers of the atmosphere above the freezing level, water will evaporate from the supercooled drops and condense on the ice crystals, thereby leading to the growth of the ice crystals at the expense of the drops. This is the celebrated Bergeron-Findeisen mechanism for the formation of large raindrops in the atmosphere. More about this mechanism will be presented in Chap. 5.