Gases as an Irreversible Process. 123 



cause the oxygen by its expansion to raise a weight, and so 

 convert part of the energy of the oxygen into mechanical 

 work W. If the gas is allowed to escape into the vacuum, 

 no such mechanical work is done, or thereafter can be done, 

 by the arrangement. We have lost an amount W of avail- 

 able energy. 



If instead of vacuum, the upper half of the cylinder be 

 rilled with oxygen at the same pressure and temperature as 

 in the lower half, no mechanical work can be done by that 

 arrangement. And therefore none can be lost by allowing 

 the two volumes of oxygen to mix by diffusion. In fact it' 

 they do mix, the whole system remains in the same physical 

 state, and therefore, by Art. 86 of Bryan's work, no entropy 

 has been gained, nor available energy lost. 



If the second half of the cylinder instead of with oxygen 

 is filled with nitrogen at the same pressure and temperature, 

 there is according to Bryan a loss of available energy for 

 each component. But it is no more possible to use the 

 oxygen-nitrogen arrangement for the practical purpose of 

 doing work than to use the oxygen-oxygen arrangement. 

 Where then is the loss of available energy when the oxygen 

 and nitrogen are allowed to mix by diffusion ? 



The explanation is probably as follows : — Bryan asserts 

 (p. 123), and he is a very high authority, (1) that when two 

 gases mix by diffusion the process is an irreversible one. 

 And I understand him to imply (2) that every irreversible 

 process is attended by a Joss of available energy. Both these 

 positions (1) and (2) seem to be disputable, even against so 

 high an authority. 



First as to the diffusion of gases being an irreversible 

 process. We know by familiar experience, that if two gases 

 mixed in different proportions but at the same pressure and 

 temperature are separated by a partition, then, when we 

 remove the partition, the gases begin to mix. That experience 

 however, so far as regards the initial stages of the process, is 

 as consistent with the diffusion being a cyclic — i. e. reversible 

 — process as with its being an irreversible one. For if there 

 be a cycle, it may be described in either of two directions, 

 ABC or CBA, one of which, in the given initial state of the 

 system, is towards, and the other from, more uniform mixture. 

 By removing the partition we determine the direction to be 

 towards more uniform mixture. For let the gases be oxygen 

 and nitrogen in a cylinder whose axis shall be that of #, and 

 let the partition be at right angles to it, the oxygen being- 

 say at the left. Before the partition is removed, oxygen 

 molecules striking it with velocity u parallel to x have that 



