Physics Laws & Theorems
Advanced

Second Law of Thermodynamics

Total entropy of an isolated system never decreases.

Formula

ΔSuniverse≥0\Delta S_{universe} \geq 0

Variables

SEntropy

Example

Disorder tends to increase

How it works

The second law says that for any isolated process, the total entropy change of the universe (system plus surroundings) cannot be negative. In practice, this happens because real processes involve irreversibilities such as friction, heat flow across a finite temperature difference, mixing, and diffusion, all of which generate entropy. A perfectly reversible process would give 0? Actually for an isolated system ? No—entropy stays constant only in the ideal reversible limit; real processes make it increase. This law is the reason heat naturally flows hot to cold and why no cyclic engine can convert all absorbed heat into work.

When to use it

Use this when analyzing whether a process is physically possible, especially for heat engines, refrigerators, phase changes, mixing, and any irreversible thermodynamic process. It is also the right tool when you need to determine the direction of spontaneous change or check whether a proposed process violates thermodynamics.

Worked example, step by step

A heat engine absorbs Q_h = 800 J from a hot reservoir at 500 K and rejects Q_c = 500 J to a cold reservoir at 300 K. Step 1: Entropy change of the hot reservoir: ? ? ? ? ? ? \Delta S_h = -Q_h/T_h = -800/500 = -1.6 J/K Step 2: Entropy change of the cold reservoir: \Delta S_c = +Q_c/T_c = +500/300 = +1.67 J/K Step 3: Total entropy change: \Delta S_universe = \Delta S_h + \Delta S_c = -1.6 + 1.67 = +0.07 J/K Step 4: Since \Delta S_universe ? 0, the process is allowed, but it is irreversible because the entropy increase is positive.

Common mistakes to avoid

  • Using the law only for the system and forgetting to include the surroundings
  • Assuming entropy must always increase, even in ideal reversible processes where the total change can be zero
  • Confusing entropy with energy and treating \u0394S >= 0 as a statement about conservation of heat or work

Did You Know?

The second law says entropy always increases, giving time its arrow and forbidding a machine that is 100% efficient.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026