Richard Becker

Fluctuations and Brownian Motion

In thermodynamics the difference in entropy of two states I and II is given by

Ideal and Real Gases

{S_{II}} - {S_I} = {\left( {\int\limits_I^{II} {\frac{{\delta Q}}{T}} } \right)_{rev}}

Lineare Schwingungen einer Kette

(73.1) where δQ is the heat supplied. The index “rev” means that the transition from I to II has to be carried out in a reversible way. If the quantum mechanical ground state E0 of the system is nondegenerate, the quantum theoretical phase volume Φ(E) approaches 1 for E just above E0, which means that the entropy, S & klnΦ, approaches zero. The entropy of the ground state can then be normalized to zero and one can define an absolute value of S by starting from the ground state E0 or from \(T = 0\left( {{S_1} = {S_{{E_o}}} = 0} \right)\):

Die Wärme als Stoff (Wärmeleitung)

{S_{II}} = \int\limits_I^{II} {\frac{{\delta Q}}{T}}

Mechanik von vielen Massenpunkten

(73.1a) .

Ein Massenpunkt im Raum

Classical thermodynamics deals only with reversible changes. The meaning of this restriction has been demonstrated in Sect. 6 by the example of a simple Carnot engine. Reversible processes have to be performed “infinitely slowly”. Any real process occurs with a finite velocity and, therefore, is necessarily irreversible. For instance, an exchange of heat between two bodies A and B is possible only if A is warmer than B, or a piston between two gas containers moves only if the pressure in the two containers differs. In both cases the actual process is associated with an increase of entropy. It is a quite strange situation that thermodynamics deals only with reversible processes which conserve the entropy of a closed system, whereas the entropy increases in all actual processes.