If we again introduce and as independent variables, then it becomes:
If we consider (1), (2) and (6), then it becomes:
or
(7)
This expression is valid in full generality.
3. The temperature of the moving body.
We first consider a system of bodies, all of them moving with the same constant velocity. Experience tells us that is then a complete differential. Equation (7) shows that this condition is satisfied, when we put
(8a)
is the integrating denominator of , when we (analogous to the preceding) understand under the temperature assumed by the body when it is adiabatically
↑Planck was the first who alluded to the fact, that the translation work must be considered in the determination of the temperature of a moving cavity.