Entropy of an Ideal Gas

Definition: Entropy of an Ideal Gas

The entropy of an ideal gas is defined as the product of the Boltzmann constant $k_B$ and the natural logarithm of the multiplicity $\Omega$ of its macrostate.

$$k_B\cdot \ln \Omega$$

NOTATION

$$S$$

Theorem: The Second Law of Thermodynamics

The infinitesimal change $\mathrm{d}S$ in the entropy of an ideal gas depends on its temperature $T$ and the infinitesimal amount $\mathrm{d}Q$ of heat which flows into it.

$$\mathrm{d}S=\frac{\mathrm{d}Q}{T}$$

PROOF

TODO