2cEntropy
Understand entropy as a measure of disorder, explore the Second Law of Thermodynamics, and discover why natural processes are irreversible.
Entropy explains why time has a direction, why engines can never be 100% efficient, and why the universe tends toward disorder — it is one of the most profound concepts in all of science.
Why do natural processes always move toward greater disorder — and what does that tell us about the direction of time?
Lesson Overview
Entropy is a measure of the disorder or randomness of a system. The Second Law of Thermodynamics states that in any isolated system, entropy never decreases — it either stays the same (reversible process) or increases (irreversible process). This lesson explores what entropy means physically, why natural processes tend toward disorder, and how probability underlies the direction of spontaneous change.
Key Concepts
Entropy (S)
A thermodynamic state function measuring disorder; SI unit: J/K
Second Law
Entropy of an isolated system always increases or stays constant
Reversible Process
Idealized process where entropy change of universe = 0
Irreversible Process
Real process where total entropy of universe increases
Entropy & Probability
High-entropy states are statistically far more probable than ordered states
ΔS = Q/T
Entropy change equals heat added divided by absolute temperature (reversible)
Worked Examples
1.00 kg of ice melts at 0 °C (273 K). The latent heat of fusion of water is 334 000 J/kg. Calculate the entropy change of the ice.
A gas expands freely into a vacuum (Joule expansion). No heat is exchanged and no work is done. Does entropy increase, decrease, or stay the same?
A Carnot engine operates between 600 K and 300 K. Is it reversible or irreversible? What is the entropy change of the universe per cycle?
Explain using probability why a drop of ink spreading through water is irreversible.
500 J of heat flows from a hot reservoir at 800 K to a cold reservoir at 400 K. Calculate the total entropy change of the universe.
Guided Problems
A 2.00 kg block of ice melts completely at 0 °C. The latent heat of fusion is 334 000 J/kg. What is the entropy change?
Hint: Use ΔS = Q/T. Remember T must be in Kelvin.
Is the process of scrambling an egg reversible or irreversible? Explain in terms of entropy.
Hint: Think about whether you can spontaneously un-scramble an egg and what that means for the number of ordered vs disordered states.
Heat Q flows reversibly into a system at temperature T. Write the formula for entropy change and state the units.
Hint: ΔS = Q/T. What are the SI units of heat and temperature?
A real heat engine rejects 400 J to a cold reservoir at 300 K and absorbs 1000 J from a hot reservoir at 700 K. Show that this process obeys the Second Law.
Hint: Calculate ΔS_hot + ΔS_cold and check whether the total is ≥ 0.
Why does a tidy room naturally become messy over time but a messy room does not spontaneously tidy itself?
Hint: Think about the number of ways a room can be 'messy' versus 'tidy' — which is more probable?
Key Vocabulary
Entropy
A thermodynamic quantity representing the degree of disorder or randomness in a system; symbol S, unit J/K.
Example: Ice melting into water increases entropy because liquid water is more disordered than the crystal lattice.
Second Law of Thermodynamics
The total entropy of an isolated system can never decrease over time; it increases in irreversible processes and stays constant in reversible ones.
Example: Heat naturally flows from hot to cold, increasing total entropy — never the reverse.
Reversible Process
An idealized thermodynamic process that can be reversed with no net change in the entropy of the universe.
Example: A Carnot engine cycle is the classic example of a reversible process.
Irreversible Process
A real process in which the total entropy of the universe increases and the process cannot spontaneously run in reverse.
Example: Gas expanding into a vacuum, ice melting, and friction are all irreversible.
Interactive Practice — 5 Questions
What does entropy measure?
The Second Law of Thermodynamics states that in an isolated system, entropy:
1000 J of heat is added reversibly to a system at 500 K. What is the entropy change?
Which process is irreversible?
Why is a high-entropy state more probable than a low-entropy state?
Independent Practice
State the Second Law of Thermodynamics in your own words and give two everyday examples of entropy increasing.
Calculate the entropy change when 500 g of ice melts at 0 °C. (Latent heat of fusion = 334 000 J/kg.)
Explain the difference between a reversible and an irreversible process. Give one example of each.
Heat flows from a reservoir at 900 K to one at 300 K. If 600 J is transferred, calculate the total entropy change of the universe.
★ A student claims that a refrigerator violates the Second Law because it moves heat from cold to hot. Refute this claim using entropy arguments, including the role of the compressor.
ChallengeCommon Mistakes
Thinking entropy always increases in every system.
Entropy of an isolated system never decreases, but a non-isolated system (like a refrigerator) can decrease in entropy as long as the surroundings increase by at least as much.
Confusing entropy with energy — "high entropy means high energy."
Entropy measures disorder, not energy. A hot gas can have high energy but relatively low entropy compared to a cold, spread-out gas.
Using ΔS = Q/T for irreversible processes.
ΔS = Q/T applies only to reversible heat transfer. For irreversible processes, ΔS > Q/T.
Math Tips
Always convert temperature to Kelvin (K = °C + 273.15) before using ΔS = Q/T.
For heat flowing out of a reservoir, Q is negative, so ΔS is negative for that reservoir. Add all ΔS values to find ΔS_universe.