The Second Law of Thermodynamics

The Second Law of Thermodynamics establishes the direction of spontaneous processes and introduces entropy as a state function that quantifies irreversibility. Key equivalent statements are the Kelvin–Planck statement (no heat engine can convert heat from a single reservoir entirely into work in a cyclic process) and the Clausius statement (heat does not spontaneously flow from a colder to a hotter body without external work). For any real (irreversible) process the total entropy of an isolated system increases; for a reversible process the total entropy is constant. The second law sets maximum limits on heat-engine efficiency and refrigerator COP and underpins exergy (availability) destruction in irreversible processes.

Governing FormulaRepresentative relations (SI units): - Entropy differential (reversible): dS = δQ_rev / T - Entropy change (general): ΔS_system = ∫(δQ_rev / T) - Clausius inequality (cyclic): ∮ δQ / T ≤ 0 (equality for reversible cycle) - Second law (isolated): ΔS_total = S_gen ≥ 0 (S_gen = entropy generation) - Carnot (maximum) efficiency for engine: η_Carnot = 1 - T_c / T_h - Carnot (maximum) COP for refrigerator: COP_Carnot = T_c / (T_h - T_c) - Entropy change for an ideal gas (constant cv): ΔS = m cv ln(T2/T1) (at constant volume) More generally for an ideal gas: ΔS = m cv ln(T2/T1) + m R ln(v2/v1) = m cp ln(T2/T1) - m R ln(p2/p1) - Exergy destruction: X_destr = T0 * S_gen (T0 = environment temperature in K) Notes/assumptions: Temperatures T in kelvin (K), heat in joules (J), entropy in J/K, use provided specific heats when needed and assume ideal-gas behavior when stated.

Knowledge Check

10 Questions

1.Which of the following is a correct statement equivalent to the Clausius form of the Second Law of Thermodynamics?

2.A reversible Carnot engine operates between a hot reservoir at 600 K and a cold reservoir at 300 K. What is its maximum possible thermal efficiency?

3.A system absorbs 5000 J of heat reversibly from a reservoir held at constant T = 400 K. What is the change in entropy of the system due to this heat transfer?

4.Heat of 2000 J flows from a body at 400 K to a body at 300 K (no other heat/work interactions). What is the total entropy change (system of the two bodies)?

5.Which mathematical statement correctly expresses the Clausius inequality for a cyclic process?

6.One kilogram of an ideal gas (assume air) is heated at constant volume from 300 K to 600 K. Using cv = 0.718 kJ·kg⁻¹·K⁻¹, what is the entropy change of the gas?

7.A refrigerator operates between an interior at 5 °C and ambient at 25 °C. What is the maximum theoretical (Carnot) coefficient of performance (COP) of this refrigerator? (Use K = °C + 273.15; give numeric approximation.)

8.Which of the following processes is isentropic (i.e., ΔS = 0 for the system)?

9.An irreversible process in a component produces entropy generation S_gen = 0.50 J/K. If the ambient (dead) temperature is T0 = 300 K, what is the exergy (availability) destroyed in the process?

10.Which of the following devices would constitute a violation of the Kelvin–Planck statement of the Second Law?