Helmholtz Free Energy

F = U - TS

Maximum work extractable at constant T and V. Also denoted A.

Variables

Helmholtz free energy

Available work at const V,T

In SI units: kg·m²/s²

Internal energy

Total internal energy

In SI units: kg·m²/s²

Temperature

Absolute temperature

Allowed values: greater than 0

Entropy

System entropy

In SI units: kg·m²/(s²·K)

J/K

Derivation

F = U - TS. At constant T,V: ΔF = ΔU - TΔS. Minimum F at equilibrium.

Your notes

0/5000

Check value

Round inputs run through this page's calculator. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.

U = 2 J (Internal energy)
T = 3 K (Temperature)
S = 4 J/K (Entropy)

Result: F = -10 J

Other thermodynamics formulas with the same quantities

Internal Energy (Ideal Gas) (First Law) shares Internal energy, Temperature
Boltzmann Entropy (Entropy) shares Entropy
Stefan-Boltzmann Law (Heat & Temperature) shares Temperature
Work (Isothermal Process) (First Law) shares Temperature
Ideal Gas Law (Kinetic Theory) shares Temperature
Ideal Gas Law (Molecular) (Kinetic Theory) shares Temperature

Where this formula is listed

Thermodynamics formulas, under Entropy, alongside Entropy Change (Ideal Gas).
In the thermodynamics list it comes after Gibbs Free Energy.
Thermodynamics formula sheet, one of 34 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Helmholtz Free Energy formula?

Helmholtz Free Energy is written F = U − TS. Maximum work extractable at constant T and V. Also denoted A. It belongs to Thermodynamics, under Entropy.

What are the units in F = U − TS?

In SI units, F is helmholtz free energy, measured in kg·m²/s²; U is internal energy, measured in kg·m²/s²; T is temperature, measured in K; S is entropy, measured in kg·m²/(s²·K).

How is the Helmholtz Free Energy formula derived?

F = U - TS. At constant T,V: ΔF = ΔU - TΔS. Minimum F at equilibrium. The result is F = U − TS.