323 
15 
The latter then determines § TT by (8) and by (11), i.e. (20), 
respectively. 
87. wc. 2 UG) is the potential energy, ey a= eh (s) 
is the thermic energy. The total energy is made up of the kinetic, the 
potential, and the thermic energies. Since the total energy of the entire 
substance is conserved, and since in the case of continuous motion the thermic 
energy is conserved in each element by (8), so in this case the kinetic plus 
potential energy of the entire substance is conserved too. In the case of 
shocks proceed like this: Let the shock be oriented in the direction of the 
flow of substance, i.e. Ml >O,. Then ‘Si a S by (13); hence 
Ome bie Cee All sides of (20) are hence positive, and so the last 
expression in (20) necessitates V, > Vy ( b= po tv) is usually convex 
from below as a function of v). (10) now necessitates b, <p, . Since 
the thermic energy increases in each element by the above, the kinetic plus 
potential energy for the entire substance decreases. 
So we see: If the thermic energy is left out of account, then the 
conservation of energy is still valid for the continuous motion, but it is 
replaced by a loss of energy for shocks. 
This explains the apparent conflict between the mechanical conser- 
vation of energy and the principles of thermodynamics in the earlier forms 
of the theory of shocks. 
According to the above, this loss of energy is better described as 
a degradation of energy. The specific degradation of energy (i.e. per unit 
mass) is 
(21) Ve eee OR een © ee 
Sika *%* 2 wx | 
the rate of degradation of energy (i.e. per unit time) is 
(22) ae bol a a 
