78 GENERAL CONDITIONS OF EQUILIBRIUM, chap.
higher pressure pu also in contact with the same liquid, and, when equilibrium has been established, let the osmotic pressure be m. We now cause a very small quantity of the gas, a gram-molecule, where a is a small number, to pass from vessel A to vessel B at constant temperature. The work done by the change of pressure is given by —
Pi
The a gram-molecule of gas is now forced into the liquid in vessel B ; for this no work is necessary, because the gas and solution are in equilibrium, and a is so small that the concentration in the liquid is not appreciably altered. On the contrary, a (negative) work A^, is done by the disappear- ance of the a gram-molecule of gas —
Ai = -l-99ar.
The gas in £ is now separated from the liquid, and by means of a semi-permeable membrane, which does not allow the gas to pass through, the liquid is allowed to take up so much solvent (vi c.c.) as is necessary to dissolve the a gram- molecule, so that the concentration is the same as that originally in B, The corresponding work is —
As = l-99ar
(and it is evident that the two last processes can be carried out in several smaller portions, whereby the whole work required to force the gas into the liquid disappears).
A quantity of liquid containing a gram-molecule of gas is removed from vessel B (the contents of which evidently return to their original condition), and this is allowed to absorb so much solvent (v — vi c.c.) that its osmotic pressure sinks from tti to ir, that which obtains in vessel A, The work done during this process is —
A^=:V99aT\n'!l
tr'
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