Second law key feature; entropy generation

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.