Entropia S = k·lnΩ
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The Boltzmann entropy calculator computes the entropy (S) of a physical system using the formula S = k·ln(Ω), where k is the Boltzmann constant (1.38×10⁻²³ J/K) and Ω represents the number of microstates. This equation is central to statistical physics, linking microscopic disorder (Ω) to macroscopic entropy. Simply input the number of accessible microstates for the system.
This tool is useful for statistical thermodynamics calculations, such as predicting entropy changes in ideal gases or irreversible processes. For instance, comparing two system states (before and after a process) helps determine if disorder increased. Entropy rises when the number of accessible microstates expands.
Ensure Ω is calculated accurately, considering physical constraints (e.g., fixed total energy). The calculator handles large Ω values numerically. Negative or zero inputs for Ω are invalid since the natural logarithm is undefined for those values.
Frequently asked questions
What is entropy in statistical physics?
Entropy (S) measures disorder or the number of microstates a system can occupy, increasing with greater disorder.
How does the calculator handle very large Ω values?
The calculator uses optimized numerical methods to process high-digit Ω values while maintaining Boltzmann constant accuracy.
Does the Boltzmann constant change across calculations?
No, the Boltzmann constant has a fixed value (1.38×10⁻²³ J/K) regardless of the system.
Can I use this for non-equilibrium systems?
The Boltzmann formula assumes thermal equilibrium; non-equilibrium systems require different models.