--- title: "Second law key feature; entropy generation" subject: "Fundamental of Thermodynamics & Heat Transfer" chapter: 5 key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:second-law-isolated-entropy-generation" source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/second-law-isolated-entropy-generation site: BCT Engineering --- # Second law key feature; entropy generation Fundamental of Thermodynamics & Heat Transfer · Chapter 5: Second Law of Thermodynamics - Asked in: 2073 Bhadra, 6 marks - Video: [Second Law of Thermodynamics - Heat Energy, Entropy & Spontaneous Processes](https://www.youtube.com/watch?v=DWiCaDPM7Hk) — The Organic Chemistry Tutor - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/second-law-isolated-entropy-generation - Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-5 ## Question What is the key feature of second law of thermodynamics? State and explain second law of thermodynamics for an isolated system. Also explain entropy generation. ## Short answer The second law gives the direction of processes and energy quality: entropy never decreases in isolation. For an isolated system, ΔS_isolated ≥ 0 (positive for irreversible, zero for reversible). Entropy generation S_gen ≥ 0 arises from irreversibilities; for any closed system ΔS = ∫δQ/T + S_gen. ## Answer #### Key feature of the second law The first law only says that energy is conserved. The key feature of the second law is that it gives the **direction** of a process and the **quality** of energy: not every process that conserves energy can actually occur. Heat flows from hot to cold by itself, never the reverse; work converts completely to heat, but heat cannot convert completely to work. The second law also sets the maximum efficiency of devices, and it introduces the property entropy. #### Second law for an isolated system Statement: *the entropy of an isolated system never decreases; it increases for every irreversible (real) process and stays constant only for a reversible process.* ΔS_isolated ≥ 0 (> 0 irreversible, = 0 reversible, < 0 impossible) Explanation: an isolated system exchanges no heat, work or mass with the surroundings, so no entropy can be transferred in or out. Entropy can only be created inside, by friction, heat flow across a finite temperature difference, mixing, free expansion and similar effects. For a system plus its surroundings (taken together as an isolated system), ΔS_universe = ΔS_system + ΔS_surr ≥ 0. This is called the **principle of increase of entropy**. Example: 100 kJ flows from a body at 500 K to one at 300 K. ΔS = −100/500 + 100/300 = +0.133 kJ/K > 0, so the process is possible. The reverse would give −0.133 kJ/K and is impossible. #### Entropy generation Entropy is not conserved. For any closed system: ΔS_system = S₂ − S₁ = ∫ δQ/T_b + S_gen - The first term is entropy **transfer** by heat across the boundary at boundary temperature T_b. It can be positive, negative or zero. - S_gen is the entropy **generated** inside by irreversibilities. S_gen ≥ 0: it is zero for a reversible process, positive for an irreversible one, and never negative. Sources of entropy generation: friction, viscosity, heat transfer across a finite ΔT, mixing, unrestrained expansion, electrical resistance, chemical reactions. For an isolated system (Q = 0), ΔS = S_gen. S_gen is a measure of irreversibility, and it is not a property (it depends on the path). The lost work is W_lost = T₀ S_gen. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. The key feature of the second law is that it: A. states that energy is conserved B. gives the direction of processes and quality of energy C. shows work cannot be converted to heat D. defines temperature Answer: B. The first law covers conservation; the second gives direction and limits. (Key point: Key feature) 2. For an isolated system, the second law states: A. ΔS ≥ 0, zero only for reversible processes B. ΔS ≤ 0 C. ΔS = 0 always D. ΔS < 0 for irreversible processes Answer: A. Entropy never decreases; it increases for irreversible processes. (Key point: Isolated system statement) 3. Why can entropy of an isolated system change only by increasing? A. Because heat flows in B. Because work is done on it C. Because mass enters D. Because no entropy transfers in or out, so it can only be created inside by irreversibilities Answer: D. With no heat, work or mass exchange, ΔS = S_gen ≥ 0. (Key point: Why entropy rises) 4. Entropy generation S_gen satisfies: A. S_gen can be negative for cooling B. S_gen ≥ 0: zero if reversible, positive if irreversible C. S_gen is always zero D. S_gen is a property of the state Answer: B. S_gen is path dependent, not a property, and measures irreversibility. 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