Laws of Thermodynamics

Zeroth Law

If two systems are each in thermal equilibrium with a third, they are in thermal equilibrium with each other. This defines temperature.

First Law — Energy Conservation

$$\Delta U = Q - W$$

The change in internal energy equals heat added minus work done by the system.

Second Law — Entropy

In any spontaneous process the total entropy of an isolated system does not decrease:

$$\Delta S_{\text{universe}} \geq 0$$

The Clausius inequality: $dS \geq \delta Q / T$.

Third Law

As temperature approaches absolute zero, the entropy of a perfect crystal approaches zero:

$$\lim_{T \to 0} S = 0$$