Practice question · Put in order
Order the statistical argument for why an isolated gas spreads out.
- Assume every microscopic arrangement of the particles is equally likely
- Count the arrangements belonging to each macroscopic state
- Group the arrangements into macroscopic states, such as the number of particles on the left
- Observe that the spread-out states own vastly more arrangements than the clustered ones
- Conclude the gas is overwhelmingly likely to be found spread out, so its entropy rises
Hints
- The argument is pure counting, and you must define what you are counting before you count it.
- The conclusion about probability comes only after the counts are compared.
Show the answer
- Assume every microscopic arrangement of the particles is equally likely
- Group the arrangements into macroscopic states, such as the number of particles on the left
- Count the arrangements belonging to each macroscopic state
- Observe that the spread-out states own vastly more arrangements than the clustered ones
- Conclude the gas is overwhelmingly likely to be found spread out, so its entropy rises
Why
The whole of the second law falls out of equal a priori probabilities plus a count. Nothing in the argument is a force or a mechanism, which is why the law is statistical and why it holds so reliably for large numbers of particles.
Practise Thermodynamics and Statistical Ideas
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More questions on Thermodynamics and Statistical Ideas
- Complete the statistical reading of the second law.
- The second law says entropy tends to increase, yet nothing in Newton's laws forbids a broken cup…
- Sort each claim by whether the second law of thermodynamics permits it.
- A fridge cools its contents while making the kitchen warmer overall. Why does that not violate the second law?