where
δE = δH + δW, δH = Tδφ,
δH being heat and δW mechanical and chemical energy imparted to the system at constant temperature; hence
| d(A − W) | = −(φ − φ0), so that A = E + T | d(A − W) | , |
| dT | dT |
which is equivalent to
| E − W = −T² | d | ( | A − W | ). |
| dT | T |
This general formula, applied differentially, expresses the heat δE − δW absorbed by a reaction in terms of δA, the change produced by it in the available energy of the system, and of δW, the mechanical and electrical work done on the system during its progress.
In the problem of reaction in gaseous systems or in very dilute solution, the change of available energy per molecule of reaction has just been found to be
δA = δA0 + R′T log K′, where K′ = b1n1b2n2 ... K;
thus, when the reaction is spontaneous without requiring external work, the heat absorbed per molecule of reaction is