Entropy
High-Yield Summary
- Entropy (S) measures disorder/randomness in a system; higher entropy = more disorder = more evenly distributed energy.
- Second law of thermodynamics: total entropy of a system + surroundings always increases in any natural process.
- ΔS = q/T calculates entropy change using heat exchanged along a reversible path.
- Entropy is called "time's arrow" — it gives natural processes an irreversible direction (energy spontaneously disperses unless hindered).
- Entropy connects to spontaneity via ΔG = ΔH − TΔS — positive entropy change of the universe corresponds to a spontaneous process.
Key Terms
- Entropy (S)
- A measure of the disorder or randomness in a system.
- Second law of thermodynamics
- The total entropy of a system and its surroundings always increases in any natural process.
- Principle of increased randomness
- Alternate name for the second law — systems evolve toward maximum disorder.
Entropy Change
ΔS = q/T
- ΔS = change in entropy
- q = heat exchanged along a reversible path
- T = absolute temperature
Gibbs Free Energy Preview
ΔG = ΔH − TΔS
- ΔG = Gibbs free energy change
- ΔH = enthalpy change
- T = absolute temperature
- ΔS = entropy change
- Full treatment of ΔG, its sign rule, and spontaneity is covered in the Gibbs Free Energy article.
Must-Know Points
- Classic example: gas confined to part of a box spreads to fill the whole box once the barrier is removed — a spontaneous shift to higher entropy. Gases never spontaneously re-confine.
- "System" for the second law can mean a single container or the entire universe — ultimately, the entropy of the universe is always increasing.
- High entropy = energy spread out evenly; low entropy = energy concentrated unevenly.
Common MCAT Trap
- The second law applies to system + surroundings together — a system's OWN entropy can decrease (e.g., water freezing) as long as the surroundings' entropy increases more.
- ΔS = q/T uses the reversible-path heat, not necessarily the actual heat exchanged in a real, irreversible process — don't plug in q for an irreversible process directly.
- Don't mix up entropy driving spontaneity alone — spontaneity depends on ΔG = ΔH − TΔS, combining BOTH enthalpy and entropy, not entropy in isolation.
Quick Recall
What does the second law of thermodynamics say about entropy?
Why is entropy called "time's arrow"?
Can a system's own entropy decrease during a spontaneous process?