Short on time? This page is the recap. For explanations, Figures 1 and 2 and the worked examples, use the full study guide.
Recap
- Entropy S describes how spread out a system’s energy is. Spread-out energy means high entropy and less energy available to do work.
- Concentrated energy spreads out by itself: hot spots even out, gases fill their containers, moving objects stop.
- Second law: the total entropy of an isolated system never decreases. It is constant only if every process is reversible.
- Real processes (friction, mixing, free expansion, heating across a temperature difference) are irreversible and raise total entropy.
- An isolated system moves spontaneously toward thermodynamic equilibrium, where its entropy is at its maximum.
- Only qualitative reasoning is needed. You never calculate entropy in this course.
Key relationships
| Situation | Entropy statement | Why |
|---|---|---|
| Isolated system, real process | ΔS_total > 0 | irreversible |
| Isolated system, ideal reversible process | ΔS_total = 0 | reversible limit |
| Isolated system at equilibrium | S at maximum; no further change | nothing left to spread |
| Closed system cooled (energy leaves by heating) | ΔS_system can be < 0 | surroundings gain at least as much S |
| Closed system heated (energy enters by heating) | ΔS_system > 0 | energy spreads into it |
| System completes a cycle | ΔS_system = 0 | state function |
| Two paths, same end states | same ΔS_system | state function; Q and W differ |
Assumptions behind the statements
- “Isolated” means no energy and no matter cross the boundary. Check the boundary before you apply the second law.
- “Closed” means energy can cross but matter cannot.
- Reversible processes are idealised: very slow, no friction, no heating across a finite temperature difference.
Mistakes to avoid
- Applying “entropy never decreases” to a closed system. It applies to the total for an isolated system.
- Thinking the second law breaks energy conservation. Energy is always conserved; the second law sets the direction.
- Saying ΔS depends on the path. The system’s ΔS does not; only Q, W and the surroundings’ changes do.
- “Q = 0, so ΔS = 0.” A free expansion has Q = 0 but ΔS_gas > 0.
- “Cold to hot is impossible.” It is impossible only spontaneously. A freezer does it using work.
- Calling every slow process reversible. It also needs no friction and no heating across a temperature difference.
Quick self-check
- Hot soup cools in a room. What happens to the entropy of the soup, the room and the total? (Soup decreases; room increases by more; total increases.)
- A gas completes a cycle. What is ΔS for the gas? (Zero: entropy is a state function.)
- A gas is heated with 400 J and does 400 J of work while expanding at constant temperature. What is ΔU? Does its entropy rise or fall? (ΔU = 0; its entropy rises because it spreads into a larger volume.)
- When is the total entropy of an isolated system constant? (Only if every process is reversible.)
Next: practice questions.