ε1 + p1v1 - p2v2 = ε2,
or
ε1 + p1v1 = ε2 + p2v2.
According to the symbols chosen by Gibbs, χ1 = χ2.
As χ1 is determined by T1 and p1, and χ2 by T2 and p2, we obtain, if we take T1 and p2 as being constant,
| ( | δχ1 | ) | dp1 = ( | δχ2 | ) | dT2. | ||
| δp1 | T1 | δT1 | p2 |
If T2 is to have a minimum value, we have
| ( | δχ1 | ) | = 0 or ( | δχ1 | ) | = 0. | ||
| δp1 | T1 | δv1 | T1 |
From this follows
| ( | δε1 | ) | + [ | δ(p1v1) | ] | = 0. | ||
| δv1 | T1 | δv1 | T1 |