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The Second Law addresses what the First Law cannot — the direction of natural processes. Two equivalent statements define it. Kelvin-Planck: no cyclic heat engine can convert 100% of absorbed heat into work; some heat must be rejected to a cold reservoir. Clausius: heat cannot spontaneously flow from a colder body to a hotter body without external work input.

Both statements are logically equivalent — violating one necessarily violates the other (provable by contradiction using a combined engine-refrigerator system). The Second Law introduces entropy $S$, defined by $dS = dQ_{\text{rev}}/T$. For any natural (irreversible) process, $\Delta S_{\text{total}} \geq 0$ — the entropy of the universe never decreases. Equality holds only for reversible processes.

Entropy is a state function: $\Delta S$ between two states is path-independent, calculated along any convenient reversible path. For an ideal gas: $\Delta S = nC_v\ln(T_2/T_1) + nR\ln(V_2/V_1)$. In free expansion, $\Delta S > 0$ even though $\Delta T = 0$ and $\Delta U = 0$ — the system disorder increases. The Second Law fundamentally limits the efficiency of all heat engines and establishes the arrow of time in thermodynamics.