Helmholtz Free Energy Calculator
Find Helmholtz free energy A=U-TS from internal energy, temperature, and entropy, the maximum extractable work at constant volume and temperature.
🧪 What is the Helmholtz Free Energy Calculator?
This Helmholtz free energy calculator finds A=U−TS from internal energy, temperature, and entropy. Enter your values, and it returns the Helmholtz free energy along with the TS term.
Helmholtz free energy represents the maximum useful work extractable from a closed system at constant temperature and volume, the constant-volume counterpart to Gibbs free energy.
With U=500 kJ, T=300 K, and S=1200 J/K, this calculator gives A=140 kJ.
This calculator is useful for physical chemistry and statistical mechanics students studying thermodynamic potentials and the partition function.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - Standard case
Example 2 - Higher internal energy and entropy
Example 3 - Negative Helmholtz free energy
❓ Frequently Asked Questions
🔗 Related Calculators
What is Helmholtz free energy?
Helmholtz free energy (A) is a thermodynamic potential representing the maximum useful work extractable from a closed system at constant temperature and volume, defined as A=U−TS, where U is internal energy, T is absolute temperature, and S is entropy.
What is the formula for Helmholtz free energy?
A = U − TS, where U is internal energy, T is the absolute temperature in Kelvin, and S is entropy. This calculator uses U and A in kJ and S in J/K, automatically converting units.
How is Helmholtz free energy different from Gibbs free energy?
Helmholtz free energy (A=U−TS) applies to processes at constant volume, while Gibbs free energy (G=H−TS) applies to processes at constant pressure. They differ by a pressure-volume term: G=A+PV, and for processes without volume change, they coincide.
What does Helmholtz free energy represent physically?
It represents the maximum work a closed system can perform on its surroundings at constant temperature and volume, part of the system's internal energy is 'unavailable' for work (bound up as TS), and A is what remains available.
Why is Helmholtz free energy important in statistical mechanics?
It connects directly to the canonical partition function Z via A=−kT ln(Z), making it one of the most important bridges between microscopic statistical mechanics and macroscopic thermodynamic properties like pressure and entropy.
When should I use Helmholtz free energy instead of Gibbs free energy?
Use Helmholtz free energy for processes at constant volume (common in statistical mechanics and closed rigid containers), and Gibbs free energy for processes at constant pressure (the more common laboratory condition, since most reactions occur in open containers at atmospheric pressure).
What does a negative Helmholtz free energy change mean?
A negative ΔA indicates the process can occur spontaneously at constant temperature and volume, analogous to how a negative ΔG indicates spontaneity at constant temperature and pressure.
Is internal energy the same as enthalpy?
No, internal energy (U) accounts for a system's total energy content, while enthalpy (H=U+PV) additionally accounts for the energy needed to make room for the system against external pressure, they are equal only when there is no pressure-volume work involved.
What units does this calculator use?
Internal energy and the resulting Helmholtz free energy are in kilojoules (kJ), entropy is in joules per Kelvin (J/K), and temperature is in Kelvin (K), matching standard thermodynamics and physical chemistry conventions.
Can Helmholtz free energy be used for ideal gas calculations?
Yes, the Helmholtz free energy of an ideal gas has a well-known closed-form expression derived from its partition function, and is commonly used in statistical mechanics derivations of the ideal gas law and related thermodynamic properties.