Out of the oven, into the frying pan

Consider a gas in the device shown above. Two halves of the box are separated by a dividing wall that has a small hole in it, which is just slightly wider than the diameter of the gas molecules. Each half of the box is in contact with a heat bath held at a given temperature.

If there are \(N\) gas molecules in the box, find the expected number of gas molecules in the hot side when the box reaches steady state.

Assumptions and Details

  • \(N=100,000\)
  • \(T_\text{High}=700\text{ K}\)
  • \(T_\text{Low}=200\text{ K}\)

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