# Thermodynamic Potentials

JoVE Core
Physik
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JoVE Core Physik
Thermodynamic Potentials

### Nächstes Video20.18: Maxwell’s Thermodynamic Relations

Thermodynamic potentials are state functions that describe the system's state as a function of thermodynamic variables.

Internal energy is a function of entropy and volume. The temperature and pressure can be expressed as a partial differential of internal energy at constant volume and entropy, respectively.

Enthalpy equals the sum of the system's internal energy and the product of its pressure and volume. Differentiating and substituting dU reduces enthalpy as a function of entropy and pressure. So, temperature and volume are obtained as the partial differentials of enthalpy.

Helmholtz free energy is given as internal energy minus the product of the temperature and the system's entropy. For an infinitesimal change, the equation becomes a function of volume and temperature. So, entropy and pressure are determined using the partial differential of Helmholtz free energy.

Replacing internal energy with enthalpy converts the Helmholtz free energy into the Gibbs free energy. Differentiating and simplifying further reduces the equation to a function of temperature and pressure. Similar calculations express entropy and volume as a partial derivative of Gibbs free energy.

## Thermodynamic Potentials

Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other two variables.

Internal energy is based on the contributions of molecules' potential and kinetic energy within a system. It is a function of entropy and volume. Therefore, the other two variables, i.e., temperature and pressure, can be expressed as the partial differential of internal energy at constant volume and entropy, respectively.

Enthalpy refers to the heat content of a system and is a function of entropy and pressure. If entropy and pressure are constant, the change in enthalpy is equal to the heat transferred to the system. For the reversible isobaric process, enthalpy represents the heat absorbed by the system. Expressions of temperature and volume can be obtained from the partial derivative of enthalpy with respect to entropy and pressure, respectively.

Helmholtz free energy measures the "useful" work obtained from a closed thermodynamic system at a constant temperature and volume. The system does work on its surroundings until its Helmholtz free energy reaches a minimum. Entropy and pressure can be expressed as the partial derivative of Helmholtz free energy with respect to temperature and pressure, respectively.

Gibbs free energy is used in problems where pressure and temperature are the important variables. It measures the maximum work done in a thermodynamic system when the temperature and pressure are constant. The expressions of entropy and volume can be obtained through partial differentiation of Gibbs free energy with respect to temperature and pressure, respectively.

## Suggested Reading

1. Blundell, S.J. and Blundell, K.M. (2010). Concepts in Thermal Physics. Second Edition. New York, US: Oxford University Press. Pp. 172.
2. Rex, A (2017). Finn's Thermal Physics. Third Edition. Boca Raton, FL: CRC Press. Pp. 163.