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Helmholtz Energy

The Helmholtz energy is a thermodynamic function of state defined by

A = U - T·S

where U is the the internal energy (Joules), T is the absolute temperature (Kelvins), and S is the entropy (Joules per Kelvin).

When a system changes its thermodynamic state, the change in Helmholtz energy is given by

dA = dU - T·dS - S·dT

If T and V are constant, then the above given differential equation can be reduced to

dA = dU - T·dS

and the combined law of thermodynamics can be reduced to

dU - T·dS ≤ 0

Therefore dU ≤ 0 (with the equality holding at equilibrium).

In other words, the Helmholtz energy of a system decreases continuously until its minimum value is reached.

The Helmholtz energy is related to the equilibrium constant at constant volume (Kv):

A = -k·T·ln(Kv)

where k is Boltzmann's constant (1.3807 × 10-23 J K-1).

If the Gibbs energy is known, the Helmholtz energy can be derived as follows:

A = G - P·(∂G/∂P)T,n

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