Unit 19: The Kinetic Theory of Gases
Pressure and temperature explained as the statistics of countless molecular collisions, from PV = nRT down to individual speeds.
5 topics · 16 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
The Ideal Gas Law
- How it worksHow do pressure, volume, temperature, and the number of gas molecules all lock together through PV = nRT?
- Worked exampleFind the pressure of 2 moles of ideal gas in a 0.05 m3 container at 300 K, using R = 8.314 J/(mol K).
- Common mistakeWhy doesn't heating a gas at constant volume require its pressure to stay the same?
- Going furtherWhat happens to a gas's pressure if its volume is cut in half while its temperature is held fixed?
Your turn1 of 2
Write an expression, in terms of n, R, T, and V, for the pressure of n moles of ideal gas in a container of volume V at temperature T, with gas constant R.Pressure From Molecular Collisions
- How it worksHow does summing up the momentum transferred by countless molecular impacts produce a steady, measurable pressure?
- Common mistakeWhy isn't gas pressure the result of molecules pushing against each other instead of against the container walls?
- Going furtherWhat happens to the pressure a gas exerts if you shrink its container while keeping its temperature fixed?
Your turn1 of 2
What is the physical origin of the pressure a gas exerts on the walls of its container?Temperature and Molecular Kinetic Energy
- How it worksHow does the average translational kinetic energy per molecule turn out to depend only on temperature?
- Worked exampleFind the average kinetic energy of a gas molecule at 300 K, using (3/2) kB T with kB = 1.38e-23 J/K.
- Common mistakeWhy doesn't every molecule in a gas at a given temperature move at exactly the same speed?
Your turn1 of 2
Write an expression, in terms of kB and T, for the average kinetic energy of a gas molecule at absolute temperature T, with Boltzmann's constant kB.The Maxwell-Boltzmann Distribution
- How it worksHow does the Maxwell-Boltzmann distribution describe the whole spread of molecular speeds in a gas at one temperature?
- Going furtherWhat happens to the shape of the Maxwell-Boltzmann distribution as a gas is heated to a higher temperature?
- Common mistakeWhy doesn't raising a gas's temperature just shift every molecule's speed up by the same fixed amount?
Your turn1 of 2
A gas is heated to a higher temperature. Does every molecule's speed simply increase by the same fixed amount, keeping the shape of the speed distribution otherwise unchanged?Mean Free Path and Diffusion
- How it worksHow does the mean free path measure the average distance a molecule travels between collisions with its neighbors?
- Worked exampleFind the mean free path of a gas molecule given a collision cross section and number density that yield lambda = 6e-8 m.
- Ties togetherHow does a short mean free path at high pressure connect to why gases start behaving more like liquids when compressed?
Your turn1 of 2
A gas has a molecular number density of 3e25 per cubic meter and a collision cross section of 5e-19 square meters. Using lambda = 1/(√2 n sigma), what is the mean free path, in meters?