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Suppose that
and
are the are the two independent parameters that specify the system.
Because

(6.100) 
we can rewrite Equation (6.82) in the form

(6.101) 
where

(6.102) 
is termed the Helmholtz free energy.
Proceeding as before, we write

(6.103) 
which implies that

(6.104) 
Comparison of Equations (6.101) and (6.104) yields
We also know that

(6.107) 
or

(6.108) 
Thus, it follows from Equations (6.105) and (6.106) that

(6.109) 
Next: Gibbs Free Energy
Up: Classical Thermodynamics
Previous: Enthalpy
Richard Fitzpatrick
20160125