Equations · Physics
Boltzmann's entropy formula
Entropy counts the microscopic arrangements that look the same from outside.
S = k_B ln Ω
Aethel says
S equals k sub B the natural log of omega
What it says
Ω is the number of microstates, the exact arrangements of molecules, that match what is observed. Entropy is proportional to its logarithm, so a system tends towards the states with the most arrangements.
It is carved, as S = k log W, on Boltzmann's tomb in Vienna.
Symbol by symbol
| Symbol | Say it | Means |
|---|---|---|
| S | S | the entropy |
| k_B | k sub B | the Boltzmann constant, about 1.381 × 10⁻²³ J/K |
| ln | the natural log of | the logarithm to base e |
| Ω | omega | the number of microstates |
More onωOmega
Where you meet it
Thermodynamics, statistical mechanics and information theory.
Questions
How do you say Boltzmann's entropy formula out loud?
S = k_B ln Ω is read: “S equals k sub B the natural log of omega.” That is exactly what Aethel says when it meets the formula in a book.
What does S mean in Boltzmann's entropy formula?
S (said “S”) is the entropy.
What does k_B mean in Boltzmann's entropy formula?
k_B (said “k sub B”) is the Boltzmann constant, about 1.381 × 10⁻²³ J/K.
Can I listen to the equations in my own textbook like this?
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