gen-define-the-second-law-of-thermodynamics-and-give-one-short-w-0230

Define the second law of thermodynamics and give one short worked example.

# Second Law of Thermodynamics **Definition:** The entropy of an isolated system never decreases over time. Entropy either increases (for irreversible processes) or remains constant (for reversible processes). Alternatively: Heat spontaneously flows from hotter to colder objects, never the reverse (without external work). ## Worked Example **Problem:** A hot cup of coffee at 80°C sits in a room at 20°C. Does the coffee warming the room or the room cooling the coffee comply with the second law? **Solution:** The total entropy change must be ≥ 0. - Coffee loses heat: ΔS₁ = -Q/T_hot = -Q/353 K - Room gains heat: ΔS₂ = +Q/T_cold = +Q/293 K Total: ΔS_total = Q(1/293 - 1/353) = Q(0.00341 - 0.00283) = +0.00058Q Since ΔS_total > 0, **the coffee cooling down is allowed** (and will happen naturally). If heat flowed the opposite way (room → coffee), ΔS_total would be negative, violating the second law. This is why hot coffee never spontaneously gets hotter in a cool room!