The Second Law of Thermodynamics explains why real thermal processes have a preferred direction. Heat naturally flows from hot objects to cold objects, and engines can convert only part of that heat into useful work. The rest must be rejected to a colder reservoir, which limits every power plant, car engine, refrigerator, and heat pump.
Entropy is the key quantity that tracks this direction and the unavoidable spreading of energy.
Key Facts
- For any cyclic heat engine, Wout = QH - QC.
- Thermal efficiency is η = Wout / QH = 1 - QC / QH.
- For a reversible Carnot engine, ηmax = 1 - TC / TH, with temperatures in kelvin.
- Entropy change for reversible heat transfer is ΔS = Qrev / T.
- For an isolated system, ΔSuniverse = ΔSsystem + ΔSsurroundings ≥ 0.
- Entropy generation measures irreversibility: Sgen = ΔSuniverse ≥ 0.
Vocabulary
- Second Law of Thermodynamics
- The principle that the total entropy of an isolated system never decreases and that heat does not spontaneously flow from cold to hot.
- Entropy
- A thermodynamic state property that measures energy dispersal and helps predict the direction of spontaneous change.
- Heat Engine
- A device that takes in heat from a hot reservoir, converts some of it to work, and rejects the remaining heat to a cold reservoir.
- Irreversibility
- A feature of real processes that prevents them from being perfectly undone without leaving changes in the system or surroundings.
- Entropy Generation
- The entropy produced inside a real process because of effects such as friction, unrestrained expansion, mixing, and heat transfer across a finite temperature difference.
Common Mistakes to Avoid
- Assuming all heat input can become work. This is wrong because the Second Law requires a heat engine to reject some heat to a colder reservoir.
- Using Celsius in Carnot efficiency calculations. This is wrong because temperature ratios in thermodynamics must use kelvin.
- Treating entropy as exactly the same as visible disorder. This is incomplete because entropy is a state property related to energy dispersal and the number of possible microscopic arrangements.
- Forgetting to include the surroundings when checking the Second Law. A system's entropy may decrease, but the total entropy of the system plus surroundings must not decrease for a real spontaneous process.
Practice Questions
- 1 A heat engine absorbs 600 J from a hot reservoir and rejects 420 J to a cold reservoir each cycle. Find the work output and the thermal efficiency.
- 2 A Carnot engine operates between TH = 500 K and TC = 300 K. What is its maximum possible efficiency, and how much work can it produce from 1000 J of heat input?
- 3 A cup of hot coffee cools in a room. Explain why this process is spontaneous and why the reverse process, where room air warms the coffee back up by itself, is not observed.