Gas Expansion & Thermal Entropy

Concept Quiz

Boltzmann's Entropy Formula

Entropy ($S$) is a measure of the number of specific ways in which a thermodynamic system can be arranged, commonly referred to as microstates ($\Omega$). A highly ordered system has few microstates and low entropy. A highly disordered, randomly moving system has vastly more microstates and high entropy.

$$ S = k_B \ln \Omega $$
Positional Entropy: When the partition is removed, the gas has twice as much volume to occupy. The number of possible positional microstates increases massively, so entropy increases spontaneously.
Thermal Entropy: Increasing temperature increases the kinetic energy. The particles occupy a wider distribution of velocity microstates, increasing entropy.