Entropy & the Second Law
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.
Heat flows on its own only from hot to cold. The deeper rule: the total entropy of an isolated system never decreases. Entropy measures how spread out energy is, so energy spreads out unless something does work to concentrate it.
1. Why heat flows hot to cold
2. What the second law allows
The entropy of one part can go down, as long as another part goes up by at least as much. A freezer lowers the entropy of the water it freezes but dumps even more into the kitchen.
Heat flowing from cold to hot on its own would lower the total entropy, so it never happens.
Other one-way processes: a gas spreading into a vacuum, ice melting in a warm room, a drop of dye spreading through water. Each increases the total entropy, and none reverses on its own.
No heat engine can turn all its heat into work; some must be released at the lower temperature.
3. Example, then try it
600 J flows from a block at 400 K to a block at 300 K. Find the total entropy change. (Treat both temperatures as constant.)
Hot block: ΔS = −600 ÷ 400 = −1.5 J/K. Cold block: ΔS = +600 ÷ 300 = +2.0 J/K.
Total: +0.5 J/K. Positive, as the second law requires.
A refrigerator removes 300 J of heat from its inside at 250 K. Its motor does 100 J of work, and it releases 400 J into the kitchen at 300 K. Does the total entropy go up or down?
Inside: loses heat, so ΔS = −300 ÷ 250 = −1.2 J/K.
Kitchen: gains 400 J (the 300 J plus the motor’s 100 J), so ΔS = +400 ÷ 300 ≈ +1.33 J/K.
Total: −1.2 + 1.33 ≈ +0.13 J/K, an increase.
So: moving heat from cold to hot is allowed because the motor’s work makes the kitchen gain more entropy than the inside loses.
Answer: up by about 0.13 J/K; the second law is satisfied.
4. Common mistakes
Can the entropy of part of a system decrease?
The second law limits the total. One part can lose entropy if the rest gains at least as much, as in a refrigerator.
Ready to practice?
5 questions on Entropy & the Second Law, each with a hint and an explanation for every wrong answer.