Unit 37: Boltzmann’s Equation & Perrin’s Experiment
Practice Problems
Note: problem difficulty is ranked using a star system.
(*) One-star problems are fundamental to the unit, and can be done relatively quickly. Use these problems to introduce yourself to the material.
(**) Two-star problems are more difficult, and require an understanding of one or two key concepts. Use these problems to test your understanding of the material.
(***) Three-star problems are the most difficult, and require some creative thinking in addition to a deep familiarity with multiple key concepts. Use these problems to challenge yourself; if you can complete one of these, you’re on your way to mastering the material.
*Q37.1) Consider a gas in a container at a constant 27°C. The particles have two different energy states: 0.2kT and 0.6kT. If 5000 particles occupy the lower energy state, how many particles occupy the higher energy state?
**Q37.2) Consider a gas in a container at a constant temperature T. The particles have two different energy states, the higher of which has energy 0.8kT. If the lower energy state has twice the population of the higher energy state, what’s the energy of the lower energy state? Provide your answer in units of kT.
**Q37.3) In an experiment similar to Perrin’s, resin particles of radius 0.05μm and density 1050 kg/m³ are suspended in a column of water at 27°C. If 500 particles per unit volume are counted at the bottom of a container, how many particles per unit volume would you expect to find 10cm above the bottom?
**Q37.4) In an experiment similar to Perrin’s, resin particles of radius 0.05μm and density 1050 kg/m³ are suspended in a column of water at 27°C. If 500 particles per unit volume are counted at the bottom of a container, at what height above the bottom would you expect to count 250 particles per unit volume?
***Q37.5) In an experiment similar to Perrin’s, 200 particles per unit volume are counted at the bottom of a container and 150 particles per unit volume are counted 5cm above the bottom. At what height above the bottom would you find 100 particles per unit volume?