Atoms in Motion

Notes from, "Chapter 1: Atoms in Motion", from The Feynman Lectures on Physics: Volume I.

1.1 Introduction

The laws of physics have changed as we have discovered new things. For example, we previously thought that an object's mass was constant, but have recently found that an object's mass increases as it approaches the speed of light.

This poses a challenge for teaching physics: it is difficult to begin with relativity, four-dimensional space-time, etc. So it is important to at least be aware of the more complex models even when learning the simpler ones.

1.2 Matter is made of atoms

Perhaps the most foundational discovery of science is that matter is made of atoms. Atoms are about $1 \times 10^{-8}$ in radius. Because of this, a unit of measurement called the angstrom (A) was put into use, which is $10^{-8}$.

Liquids stay together because of molecular attraction. When we increase the temperature of water, the speed of individual molecules and the volume between the $H_2O$ molecules increases. With enough heat, this motion is enough to overcome the force of molecular attraction and turn water into steam.

Water vapor (or any gas) exerts a force on the walls of an enclosed space due to the collisions of its molecules against the wall. While the force technically varies because the collisions aren't consistently pushing against the wall in the same direction, they occur often enough to exert an average force.

If we imagine a piston at the top of a cylinder containing water vapor, we must apply some downward force to keep the piston in place. From this, we get pressure, which is the force per unit area over which that force is applied.

If we were to increase the area of the piston while keeping the total volume of the cylinder constant, the downward force we apply to the piston would need to increase, because we have increased the number of molecules that collide with the piston.

If we double the number of molecules in the tank, we increase the density, where density ($\rho$) is defined as the amount of mass per the volume the mass is contained in.

Because there are now more molecules around to collide with the piston, we can say that density is directly proportional to pressure.

Similarly, if we were to increase the temperature of the water vapor, the speed of the molecules would increase and collide with the piston more frequently, which would increase the amount of force we would need to apply to keep the piston in place. Hence, temperature is also directly proportional to pressure.

If the piston were to move downward and compress the gas, it would collide with the molecules and increase their speed. This means that compressing a gas will increase its temperature, and expansion will decrease it.

At very low temperatures, water molecules will lock together to form ice. Solids arrange their molecules in a crystalline array, where there is a fixed place for every atom. $H_2O$ shrinks when it melts because its crystalline structure as a solid has a lot of gaps. This is unlike many other substances.

While molecules are locked in a crystalline array, they still vibrate in accordance to their temperature. When the temperature is high enough, molecules will break free and the substance will melt.

All liquids will freeze at absolute zero, except for helium, which requires a great increase of pressure as well to force the atoms to lock together.

1.3 Atomic processes

The air we breath consists almost entirely of nitrogen ($N_2$), oxygen ($O_2$), some water vapor, carbon dioxide, argon, and a few other things.

Salt is not made up atoms per se, but of ions. Ions are atoms that either are missing or have extra electrons. The sodium and chlorine ions in salt stick together by an electrical force, but separate to dissolve in water. In this sense, we wouldn't necessarily call $NaCl$ a "molecule", since it's not held together by atomic forces. Intead, it's typically referred to as a chemical compound.

1.4 Chemical reactions

A process that results in the rearrangement of atoms is called a chemical reaction. The energy of carbon snapping onto to oxygen is how we get fire and flames.

Brownian motion has helped us tell that atoms are present — the motion of a slightly larger object detectable by microscope will move.