Overview
This lecture discusses entropy from a microscopic (statistical) perspective, provides examples of entropy change in different systems, and introduces the third law of thermodynamics.
Entropy and Disorder on a Microscopic Scale
- Entropy measures the disorder or randomness of a system; more disordered systems have higher entropy.
- Shuffling a deck of cards increases its entropy by creating a more random arrangement.
- The second law of thermodynamics states that entropy of the universe increases in any irreversible process.
- Irreversible processes, like the free expansion of a gas, increase disorder (and thus entropy).
Calculating Entropy Change: Examples
- The entropy change for a system can be found by imagining reversible processes between initial and final states.
- For melting ice and warming it, entropy increases by both the phase change and temperature increase.
- The entropy lost by a heat reservoir is smaller than the entropy gained by the ice, so total entropy of the universe increases.
Biological Order and Entropy
- The organization of living things does not violate the second law; local ordering is offset by greater disorder elsewhere.
- Overall, the net entropy change for the universe is still positive even when complex order appears locally.
The Third Law of Thermodynamics
- The third law states that absolute zero temperature cannot be reached in a finite number of steps.
- As temperature approaches absolute zero, the entropy of a system approaches a minimum value.
- Reaching 0 K is fundamentally impossible due to quantum effects; achieved temperatures approach but never reach 0 K.
- If a reservoir existed at 0 K, engines could be 100% efficient, violating the second law.
Example Problems
- In adiabatic free expansion of an ideal gas, entropy increases because the gas spreads into a larger volume.
- When two objects of different temperatures exchange heat, the net entropy change is positive.
- Entropy change for heating/cooling is found using ΔS = mc ln(T_final/T_initial).
Key Terms & Definitions
- Entropy (S) — A measure of disorder or randomness in a system; higher when arrangements are more random.
- Irreversible process — Process that increases the entropy of the universe; cannot be wholly reversed.
- Second law of thermodynamics — Entropy of the universe never decreases in any thermodynamic process.
- Third law of thermodynamics — Absolute zero cannot be reached through any finite number of cooling steps.
Action Items / Next Steps
- Review and practice calculating entropy changes for melting, heating, and free expansion cases.
- Answer “Check Your Understanding” questions to solidify understanding of entropy change in heat transfer.
- Explore the recommended interactive site to see entropy changes with microstates.