Episode 601: Brownian motion and ideal gases

This episode looks at Brownian motion as evidence for the particulate nature of matter, and the macroscopic gas laws.

Summary

  • Demonstration and discussion: Brownian motion and what this tells us about air (and other gases) (30 minutes)
  • Demonstration and student experiments: The gas laws (60 minutes)
  • Discussion: Boyle’s law – a particle explanation (20 minutes)
  • Discussion: Extrapolating to absolute zero (10 minutes)
  • Student activity: A computer model of Boyle’s law (20 minutes)

Demonstration and discussion: Brownian motion and what this tells us about air (and other gases)
A reasonable place to start is by reviewing the evidence that matter is made up of particles (molecules and atoms). (It is probably best to refer to ‘particles’ in general, and to think of them as spherical; point out that, by this, we mean either atoms or molecules.) Students will have met these ideas at a lower level in chemistry as well as physics. Evidence includes the combination laws of gases, and Brownian motion, which can be demonstrated in the classroom.

According to your students’ previous experience, you may wish to demonstrate Brownian motion, the expansion of bromine into a vacuum, and a measurement of the density of air.

Episode 601-1: Brownian motion in a smoke cell (Word, 58 KB)

Episode 601-2: Diffusion of bromine (Word, 72 KB)

Episode 601-3: The density of air (Word, 72 KB)

Brownian motion is evidence not just for the existence of atoms or molecules but also for their movement, which is random. This random motion can be modelled mathematically and leads to a test for the size of the atoms from measured diffusion rates – this was one of Einstein’s great papers of 1905.

Question: What is the mass of air in the room? Answering this will require the estimation of the volume of the room, and the use of the density of air. Students are often surprised by the result: perhaps 100 kg, more than the mass of a typical student. If all of the air in the room condensed to form a liquid, it would make a layer perhaps 5 mm deep on the floor.

Now you can introduce a gas as a simple system. In crystalline solids, all the atoms are nicely ordered in an array, making calculations possible. In a gas, the motion is random and again this simplifies calculations as the laws of statistics can be applied. (Disordered solids and liquids are more difficult to treat mathematically, because they are neither well-ordered nor completely disordered.)

Equipment to demonstrate Boyle’s law

Demonstration and student experiments: The gas laws
Now move on to the gas laws. Strictly speaking it is only necessary to look at Boyle’s law (PV = constant at constant temperature).

You may well have an apparatus specifically designed to show this such as an oil-filled column attached to a pump and pressure gauge. You pump air in to pressurise the oil, which compresses an air space at the top. A series of about 10 P and V readings usually gives a good fit to a straight line when P is plotted against 1/V.

Episode 601-4: Changes in volume, changes in pressure (Word, 58 KB)

The other laws follow from this and the definition of thermodynamic temperature. However, at this stage it is likely that the only idea of temperature students are familiar with is “that which is measured by a thermometer”. (This is not a totally silly definition as it relies on the fact that when two bodies of different material, temperature and size are in contact, their temperatures equalise. This is usually referred to as the Zeroth Law of Thermodynamics.)

Equipment to demonstrate Charles’ law

So it is worth pressing ahead with demonstrations or class experiments of Charles’ law (V proportional to T) and/or the pressure law (P proportional to T).

Episode 601-5: Changes in temperature, changes in pressure (Word, 96 KB)

Episode 601-6: Changes in temperature, changes in volume (Word, 112 KB)

Discussion: Boyle’s law – a particle explanation
You may need to discuss how Boyle’s law can be explained in terms of particles.

Episode 601-7: Boyle’s law, density and number of molecules (Word, 65 KB)

Discussion: Extrapolating to absolute zero
Both Charles’ law and the pressure law lead to the concept of an absolute zero of temperature. Note that Absolute Zero (0 K) is the temperature at which the energy of the particles of a material has its minimum value; this is not zero, as the particles have so-called zero point energy due to quantum effects, which cannot be removed. They still vibrate.

Remember real gases turn into liquids and solids before absolute zero is reached. However extrapolating back often gives reasonable values.

Episode 601-8: Changing pressure and volume by changing temperature (Word, 53 KB)

Episode 602: Ideal gases and absolute zero (Word, 56 KB)

Student activity: A computer model of Boyle’s law
If suitable apparatus for demonstrating Boyle’s law is not available it can be simulated using computer packages or applets but this is a poor relation to the real experiment and should only be used to illustrate the effect, not to demonstrate it.

See a model on the Salve Regina University website.

Download this episode
Episode 601: Brownian motion and ideal gases (Word, 499 KB)