Residual Entropy

\[SR=S-Sig\]

Variables

SRresidual entropy (J/(mol·K))

Sreal-gas entropy (J/(mol·K))

Sigideal-gas entropy at same temperature and pressure (J/(mol·K))

Description

What is this formula?

Residual entropy is the difference between the entropy of a real fluid and the entropy that the same substance would have if it behaved as an ideal gas at the same temperature and pressure.

When to use it

Use this equation when evaluating thermodynamic properties of real gases, performing equation-of-state calculations, or correcting ideal-gas entropy estimates for non-ideal behavior.

Example

A gas has a real entropy of 185 J/(mol·K). The corresponding ideal-gas entropy at the same temperature and pressure is 192 J/(mol·K).

Formula:

SR = S - Sig

Substitution:

SR = 185 - 192

Result:

SR = -7 J/(mol·K)

The real gas has an entropy 7 J/(mol·K) lower than the corresponding ideal gas.

Applications

- Equation-of-state calculations

- Vapor-liquid equilibrium studies

- Natural gas processing

- High-pressure thermodynamics

- Process simulation software

Note

Residual entropy is not measured directly. It is typically calculated using equations of state such as Peng-Robinson, Soave-Redlich-Kwong, or virial models. As pressure decreases and ideal-gas behavior is approached, the residual entropy tends toward zero.