(3) |
(4) |
(5) |
In the differentiation of one of the quantities , the two others have to be kept constant. We also emphasize, that we understand as the energy which it obtains when the body is brought adiabatically and isochorically to rest; the way by which the body has acquired its momentary (moving) state, is completely irrelevant.
1. Computation of the pressure.
We denote the pressure of the resting system by , that of the moving one by . In order to compute the latter, we consider the following circular process:
A. The initial state shall be that of rest; shall be the values of the relevant state variables. We change the volume adiabatically from to ; then the energy assumes the value .
B. We bring the body to the velocity . The energy assumes the value
The work of the external forces is
.
C. We change (at constant velocity) the volume adiabatically by . The external forces perform the compression work and the translation work (in order to keep the velocity constant). Thus the increase of energy is
.