APPENDIX: AN EXAMPLE OF MAXWELL'S EXPLANATORY STRATEGY

Examining the Clausius equation given in section 2, we may conclude that the pressure of a gas depends on the kinetic energy T of the system of molecules, which is due to the motion of the molecules and to the quantity 1/2Rr, which depends on the forces between them.

containers would be greater in a larger container than in a smaller one, and greater in the open air than in any container, which is contrary to what is observed. If we suppose that the molecules of the gas do not ex­ert any forces on each other, then the Clausius virial equation reduces to pV = 2/3T. Then since T is the kinetic energy of the system of particles, where M is the mass of the gas, i.e., the mass of the system of molecules, and since T = 1/2Mc², where c is the mean velocity of a molecule, Max­well derives the equation pV = 1/3Mc². The latter is Boyle's law, on the assumption that the temperature of a gas is proportional to the mean kinetic energy of the molecules.

Now, continues Maxwell, it is known that real gases deviate from Boyle's law at low temperatures and high densities. And he asks whether the second factor in Clausius's equation dealing with forces between molecules, which was ignored in deriving Boyle's law, can be invoked to explain actual deviations from that law found in experiments. These ex­periments show that as the density of a gas increases, its pressure is less than that given by Boyle's law. Hence, the forces between the molecules must on the whole be attractive rather than repulsive. In the virial equa­tion this is represented by a positive virial. Experiments also show that as the pressure of a gas is increased, it reaches a state in which a very large increase in pressure produces a very small increase in density, so that the forces between molecules are now mainly repulsive.^[233]

acknowledgment For sharp criticisms and very helpful suggestions, I am indebted to Linda S. Brown, Victor DiFate, and Richard Richards.