The free energy as an example for a thermodynamic potential

1.13 The free energy as an example for a thermodynamic potential

The free energy is the corresponding thermodynamic potential for the thermal contact of section 1.9.
The corresponding coordinates are therefor $V, N$ , and $T$ .
It is well known that

$F (V, N, T) = U (V, N, T) - S (V, N, T) T$

(1.17)

and

$d F = μ d N - p d V - S d T$

(1.18)

Mathematical interpretation: total differential, partial derivative


${\frac{\partial F}{\partial N} \|}_{V, T} = μ$	${\frac{\partial F}{\partial V} \|}_{N, T} = - p$	${\frac{\partial F}{\partial T} \|}_{V, N} = - S$

Physical interpretation: gradient, forces


$μ$ : ”force” changing the particle number	$- p$ : ”force” changing the volume	$- S$ : ”force” changing the temperature

here:	$V, N, T$ :	generalized coordinates
	$- p, μ, - S$ :	generalized forces

For ”normal” physical quantities:
Coordinates: extensive parameters
Forces: intensive parameters
Forces and coordinates can be exchanged. There exists no principle difference between these parameters since they are equivalent and just depend on the choice of the thermodynamic contact.

[next] [prev] [prev-tail] [front] [up]