Page:Zur Dynamik bewegter Systeme.djvu/2

 heat radiation, a separation of energy into internal and progressive energy is quite impossible, although its energy notably depends on the speed of motion; therefore such a separation of the total energy is not feasible. Although the internal radiation energy might have superiority in most cases over other energy forms, the latter will be nevertheless always present in detectable quantities and under well realizable circumstances even of the same order. For gaseous bodies its amount is most notable. Take for example an ideal one-atomic gas at rest under the pressure p at temperature T, then the radiation energy within the gas is aVT4, that is in absolute C.G.S. system, a = 7,061·10-15 and $$V=\frac{RNT}{P}$$ (N is the number of moles, R = 8.31·107). In contrast, the internal energy of the gas, so far as it arises from the kinetic energy of molecular motions, is: NcvT+ const., where the molar heat cv at constant volume in the same system of units is equal to 3 · 4.19·107 = 1.257·108. So if we supply heat to the gas from the outside at constant volume, then heat is distributed over the two mentioned energy forms in the ratio:

$$\frac{4aVT^{3}}{Nc_{v}}=\frac{4aRT^{4}}{c_{v}p}$$.

For 0.001mm of pressure at the temperature of melting platinum, in absolute measure p = 1,33 and T = 1790 + 273 = 2063, this proportion will be equal to 0.25 by using the given numbers; that is to say, in a heated one-atomic gas (by using the assumed values of pressure and temperature) the heat which causes an increase of radiation energy is already the fourth part of the heat due to molecular motions.

Another example concerns the inertial mass of a body. The concept of mass as an absolutely immutable quantum, neither modifiable by any physical nor by chemical influences, belongs to the foundations of mechanics since Newton. It appears that we can attribute constancy to it before all other quantities: it is what until very recently, even in 's mechanics, was considered to be the fundamental property of matter and therefore is used in almost every physical world system as the first building stone. However, it can now be proven that the mass of each body depends on temperature. Because inertial mass is defined most directly by the kinetic energy. But since it is, as shown earlier, impossible to separate the energy of the