Entropy and the Second Law of Thermodynamics

Since $Q_H/T_H=Q_L/T_L$ for a Carnot engine, the quantity $Q/T$ is called entropy -- a state variable, with $Q_H/T_H$ the entropy received from the hot reservoir and $Q_L/T_L$ the entropy given out to the cold reservoir; for a reversible (Carnot) engine these are equal, so its entropy change over one cycle is exactly zero. For every real, irreversible engine (diesel, petrol), the corresponding entropies instead satisfy $Q_L/T_L>Q_H/T_H$, motivating a more general restatement of the second law: "For every process that actually occurs in nature (irreversible processes), the total entropy always increases; only for a reversible process does entropy remain unchanged." This is also why heat only ever flows from hot to cold and never the reverse -- that direction is exactly the one that increases the combined entropy of both bodies, while the reverse flow would decrease it, violating the second law. Entropy is often described as a mea …