Note 14 — Chapter II · OSMOTIC PRESSURE AND THE THEORY OF SOLUTION I

As a result of numerous vain endeavors, as well as of much direct evidence of a positive character, the scientific world has, for many years, held the opinion that any sort of "perpetual motion machine" is impossible. Every one now admits that a machine which would be able to work continuously, without consuming energy, is an impossibility—that is, that a "perpetuum mobile of the first class," as it is called, is impossible (law of the conservation of energy or first law of thermodynamics). From this law it does not of necessity follow, however, that it would be impossible to make a machine or device that would convert continuously into available energy or work, say, the enormous amounts of heat energy of the earth or of large bodies of water ("dissipated energy") which would thereby be cooled below the temperatures of their surroundings. Such a hypothetical process has been termed a "perpetuum mobile of the second class"; it has never been realized and is universally conceded to be an impossibility; the so-called "second law of thermodynamics" gives expression to this fact.

Now van 't Hoff [Z. phys. Chem., 1, 481 (1887)] showed, first, that a gas like oxygen, nitrogen, hydrogen, etc., which is soluble in proportion to its gas pressure (Henry's law), must exert, in solution, an osmotic pressure equal to the gas pressure, which it would have, if present in the same quantity as a gas in the same volume at the same temperature; for, if such were not the case, the solution and gas could be used to produce a perpetuum mobile of the second class, which, according to the above law, is an impossibility. Similar proofs were given by Rayleigh [Nature, 55, 253 (1897)] and by Larmor [Phil. Trans., 190, 266 (1897), Nature, 55, 545 (1897)] that the principle applies to solutions of other solutes.

Provided, then, that we have (1) perfect semipermeable membranes, (2) sufficiently dilute solutions, and (3) none but negligible heats of dilution (p. 12), van 't Hoff's generalization, concerning the relation of osmotic pressure and the laws of gases, must hold, if the perpetuum mobile of the second class is impossible, as is demanded by the second law of thermodynamics.