Kinetic-Molecular Theory

Problems

practice

1. How about a simple, straightforward problem?
   1. Compute the rms speed of an oxygen molecule at room temperature.
   2. Use the results of part a. to determine the rms speed of a hydrogen molecule at room temperature.
   3. Use the results of part b. to determine the rms speed of a mercury atom at 1200 K.
2. Write something else.
3. Write something different.
4. Derive the law of Dulong and Petit by applying the equipartition of energy to the atoms in a solid.

numerical

1. What is the rms speed of a hydrogen atom in the interplanetary medium (the thin, cold plasma between the planets) if it has a temperature of 16 K?
2. What is the speed of a typical free electron in copper at room temperature? (Free electrons in a metal are those which are so loosely bound that they wander from atom to atom like the molecules in a gas.)
3. Weapons grade uranium is enriched by the diffusion of gaseous uranium hexafluoride (UF₆) through a stack of tight metal screens. The lighter, fissionable isotope ²³⁵U has a slightly faster rms speed and is more likely to diffuse through the screens than the heavier, non-fissionable isotope ²³⁸U. Determine the ratio of the rms speed of UF₆ made from the light, desirable isotope to the heavier, undesirable isotope.
4. A lead bullet weighs 4.5 g and is fired from a rifle at 914 m/s. The propellant heats the bullet to 50 °C. Determine the following quantities…
   1. the kinetic energy of the bullet
   2. the number of moles of lead in the bullet
   3. the total internal kinetic energy of the bullet
   4. the rms speed of the lead atoms in the bullet
5. A 1 m³ box contains 1 mol of helium at 727 °C. The box sits in a standard temperature and pressure (STP) environment. The box is airtight, but not thermally isolated (that is, heat can flow through the walls of the box). The box has a door on it that can open inward or outward when the airtight seal is broken.
   1. Determine…
      1. the rms speed of the helium atoms in the box
      2. the total internal energy of the helium atoms in the box
      3. the pressure on the inside walls of the box
   2. Is the net direction of heat flow into or out of the box? Justify your answer.
   3. Will the door on the box swing inward or outward when the seal is broken? Justify your answer.
6. In 2015, physicists at Stanford University in California set a new record low temperature — an ensemble of 100,000 rubidium atoms cooled to 50 pK. Determine…
   1. the rms speed of the atoms
   2. the total internal energy of the ensemble