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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