Maxwell-Boltzmann distribution

The matter around us is primarily present in either of the three states,

1. solid,
2. liquid, and
3. gas

Although the plasma state and the Bose-Einstein condensate exist, these three are the most common states of matter on Earth. The three states behave very differently with varying degrees of attractive forces and the nature of forces at play. Although every element in the periodic table can have the three primary states, not all can have the Bose-Einstein condensate state.

As an example, we can look at the water.

Water and its three states

Water is essential to life as we know it. Life is theorized to have begun with the arrival of water from outer space. Water was contained in small pockets within the comets that crashed on the Earth during the early phases of the planet’s formation.

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The figures show the water as it appears in its solid form by freezing liquid water and water vapors. On the other hand, if we give heat to the water molecules, they turn into gas. These changes of state in the water are given specific names as shown.

Some common examples of states of water found on Earth are,

• glaciers, sea ice, hail, snow for solid,
• rivers, seas, oceans, and fog for liquid, and
• water vapors for the gaseous state of water.

Temperature and the changing state of matter

A mutual variable within all the phenomena is temperature change. The introduction of temperature in matter changes the velocity of its molecules. It, in turn, changes the state of matter at hand. When providing heat to the ice, we speed up its molecules, and at some point, they break down the forces that bind them in their solid form. Similarly, if we take away the temperature from gas, we slow down the molecules, and eventually, they get slow and close enough to get captured by the binding forces, thus forming a liquid.

Although it is easy to understand how a temperature change would cause the molecules to speed up or slow down, it is essential to understand that not all the molecules will be affected equally. For a gas, even at an elevated temperature, some molecules will have very low speeds compared to the rest due to collisions. As a result, they’ll lose some of their energy to their surroundings or other molecules.

The problem with determining the speed of molecules

Let’s switch to air as an example. For simplicity, we assume that the air consists of 78% nitrogen and 22% oxygen. Since the two molecules have a different weight \(14.0067\,\text{u}\) and \(15.999\,\text{u}\) respectively, they get differently affected by the temperature change. The molecules will have different speeds even among the same type of gas. Considering there is an Avogadro’s number of molecules present in just one mole of either gas \(6.02214076\times10^{23}\) molecules per mole, we can not measure individual speeds. Instead, we consider the speed distribution within the gas at a given temperature.