Thermodynamics is the macroscopic theory of heat, work, and energy. Its core laws:

• Zeroth law: thermal equilibrium is transitive — temperature is well-defined.
• First law: $dU = \delta Q - \delta W$. Energy is conserved; heat $\delta Q$ and work $\delta W = p\,dV$ are path-dependent, but $U$ is a state function.
• Second law: $dS \geq \delta Q / T$ (equality reversible). The entropy of an isolated system never decreases. Equivalent (Kelvin) formulation: no engine working in a cycle can convert heat from a single reservoir entirely into work.
• Third law: $S \to 0$ as $T \to 0$ for a perfect crystal.

The Carnot cycle — two isotherms + two adiabats — has efficiency

the maximum possible for any heat engine running between hot and cold reservoirs at $T_H, T_C$.

Interactive: Carnot cycle on a PV diagram