Читать книгу Geochemistry - William M. White - Страница 44

Let's now return to our function β. The macroscopic function having the property of our new function β is temperature. The relation of temperature to β is

(2.53)

and

(2.54)

equation 2.53 provides a statistical mechanical definition of temperature. We can easily show that T is the measure of the energy per degree of freedom. To do this, though, we need one other relationship, which we introduce without proof. This is that Ω increases roughly with E as:

where ƒ is the number of degrees of freedom of the system (which, in turn, is proportional to the number of atoms or molecules in the system times the modes of motion, e.g., vibrational, rotational, translational, available to them). Hence:

(2.55)

Substituting , then

In other words, the temperature of a system is proportional to its energy per degree of freedom.