the heat supply.
(3) Two gases (1) and (2) thermally connected, are maintained at same temperature but different pressure and change adiabatically while experiencing change of volumes; then it can be shown that for this finite change,
, that is for the two gases the sum of the final
No other change is effected in any other bodies but in these two gases; here emphasis is laid on preposition in; for the work done may be the lifting or lowering of a load and such change of location in rigid bodies involves no change of inner energy. Changes of density in external bodies can be also avoided by having the two gas tanks located in a vacuum.
(4) A similar proposition can be established for a system of any number of gases by successively treating the gases in pairs as above. The theorem then reads: "If the gas system as a whole possesses the same entropy in two different states then the system can be brought from one state to the other in a reversible manner without changes remaining in other bodies."
(5) We know that the expansion of an ideal gas without doing external work and receiving any heat supply is an irreversible process. The consequence is that the entropy of this gas increases. It follows at once that "it is impossible to diminish the entropy of an ideal gas without changes remaining in other bodies."
(6) The same result obtains for a system of any number of ideal gases. Consequently "there exists in the whole of Nature no means (be they of the mechanical, thermal, chemical or electrical sort) of diminishing the entropy of a system of ideal gases, without changes remaining in other bodies."