The intermolecular pair potentials of many substances are similar in shape and certainly share the same gross features of a steep repulsive wall at short distances with an attractive region at larger distances. It turns out to be extremely useful to make the two assumptions that all substances have the same form of intermolecular potential but differ in the values of energy and distance scaling parameters and, secondly, that the properties of a substance depend only upon the pair potential. Thus, we can write, for any substance, its pair potential u_{ii}(r) as
where u_{oo} is a reference pair potential, f_{ii} is an energy scaling parameter and a distance scaling parameter. It follows from these assumptions [Bett et al. (1975)] that the pressure of the pure fluid i may be obtained from the pressure of the pure fluid o by means of the equation
This result pertains for any substance i that is part of the set for which the pair potentials are conformal. It follows that the reduced pressure p_{i}h_{ii}/f_{ii} is the same function of the reduced variables and T/f_{ii} for all substances in that set. This means that if is known for one substance in the set of conformal substances, the pressure can be calculated for other substances from a knowledge only of the scaling parameters h_{ii} and f_{ii}. Very often the scaling parameters h_{ii} and f_{ii} are taken to be the critical volume and critical temperature of the fluid respectively, although this is not essential.
In as much as the assumptions upon which the development of the principle of corresponding states is based are not satisfied by any real fluid, the principle itself is obeyed only approximately. Nevertheless, it is a very powerful tool for the estimation of the properties of fluids [Reid et al. (1977)] and has been extended to the treatment of nonspherically symmetric molecules.
REFERENCES
Bett, K. E., Rowlinson, J. S. and Saville, G. (1975) Thermodynamics for Chemical Engineers, Athlone Press, London.
Reid, R. C, Prausnitz, J. M. and Sherwood, T. K. (1977) The Properties of Gases and Liquids, McGraw-Hill, New York.
References
- Bett, K. E., Rowlinson, J. S. and Saville, G. (1975) Thermodynamics for Chemical Engineers, Athlone Press, London.
- Reid, R. C, Prausnitz, J. M. and Sherwood, T. K. (1977) The Properties of Gases and Liquids, McGraw-Hill, New York.