As material is transported upwards through the troposphere, temperatures drop and for some gases the partial pressure becomes equal to the saturated vapor pressure. Assuming the presence of cloud condensation nuclei, which appear abundant in the giant planet atmospheres, cloud layers may form and the gaseous abundance of the condensing molecules falls according to the saturated vapor pressure. For simple liquid/vapor and solid/vapor transitions, the condensation levels of clouds may be easily estimated from simple thermodynamics.
The Clausius-Clapeyron equation, which governs how pressure p and temperature T vary along a first-order phase transition, is given by (e.g., Finn, 1993)
where AS is the change in entropy of a certain quantity of material changing phase; and AV is the associated change in volume. For the liquid-vapor and solid-vapor phase boundaries, where the volume of the gas phase greatly exceeds that of the liquid or solid phases, AV is approximately the volume of the gas phase alone and thus Equation (4.45) is well approximated by
where the ideal gas equation has been assumed and where L is the latent heat of vaporization per mole and R is the molar gas constant. If L is assumed not to vary with temperature then this equation may be simply integrated to give
where A and - are constants that may be fitted to the measured saturated vapor pressure curves. More generally, the latent heat L varies with temperature also, which introduces extra terms into Equation (4.47). However, these are secondary effects and for the case of giant planet atmospheres, where many constituents may condense whose phase boundaries have not been measured with very great precision, they are usually neglected. The fitted coefficients A and - for a number of first-order phase transitions relevant to the giant planet atmospheres are listed in Table 4.5.
In addition to the simple condensation of vapor into liquid or solid aerosols, more complex two-component reactions may occur such as the formation of solid ammonium hydrosulfide (Equation 4.10). The thermodynamics of this are more complicated, but the variation in vapor pressure of both reactants with temperature may be adequately approximated by a similar equilibrium constant equation to Equation (4.47)
where pNH3 and pH2S are the partial pressures (in bar) of NH3 and H2S, respectively. Since this equation has two unknowns, we need additional information, which comes from the fact that we know that one molecule of NH3 reacts with one molecule of H2S
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