What Is Temperature?
What is temperature? It is a direct measurement of the average translational kinetic energy of an assembly of ideal gas molecules. The air around us behaves almost exactly like an ideal gas under normal conditions. Therefore, that definition applies directly to our everyday world.
Two Equations Relating Temperature to Kinetic Energy
The mathematical equation expressing temperature with respect to the average translational kinetic energy of the assembly is
where
T = absolute temperature (in kelvin)
Ktotal = translational kinetic energy of the entire assembly (in joules)
N = total number of ideal gas molecules in the assembly
kB = Boltzmann constant (≈ 1.38 x 10-23 J/K)
This equation shows that T depends only on Ktotal and N.
When the assembly has reached a stable macroscopic state (called thermal equilibrium), the translational kinetic energy of the entire assembly of ideal gas molecules taken at an instant divided by N is identical to the average translational kinetic energy of one ideal gas molecule taken over a period.
Why? The molecules are constantly colliding and exchanging energy. A single molecule will eventually cycle through every possible energy state that exists across the assembly. Therefore, looking at the entire assembly at one split second gives us the same average as tracking one molecule’s long, chaotic journey over time.
Therefore, the equation for T becomes
where Kavg = Average translational kinetic energy of a single molecule (in joules)
A Macroscopic Window into the Microscopic World
What is temperature? It is also a direct, macroscopic measurement of a microscopic property: Kavg. T is directly proportional to Kavg. The equation for T has a constant scaling factor (2 ÷ 3kB) and no other variables. Therefore, T and Kavg are fundamentally the same property. No other variables (e.g., mass of the gas, volume of the container) appear in that equation for T. Therefore, changing Kavg changes T by the same factor. Hence, temperature is a macroscopic window into the microscopic world.
Temperature Is Independent of Assembly Size
Moreover, temperature is independent of assembly size. Consider a small balloon of room-temperature air and a giant enclosed stadium filled with room-temperature air. They are both at 20°C. That temperature reveals how energetic on average the air molecules are, completely independent of the size of their container.
What Temperature Does
In addition, temperature does two important things:
- It filters out fluctuations in translational kinetic energy of individual molecules. (For example, one molecule may be moving slowly, and another may be moving fast.) Imagine checking an outdoor thermometer mounted on a porch to see the weather. The device sits immersed in a massive, invisible assembly—the surrounding air. Trillions of gas molecules bombard the thermometer constantly. The temperature shown ignores completely individual fluctuations in translational kinetic energy and tells us the average translational kinetic energy of the entire assembly.
- It dictates the direction of energy flow. If we bring two different assemblies together—say, hot air and a cold metal spoon—their temperatures tell us exactly how they will interact. The molecules of the high-temperature assembly have a higher average translational kinetic energy than the molecules of the low-temperature assembly. Thus, when the molecules of the former assembly collide with the molecules of the latter assembly, the former assembly transfers energy until both assemblies have the same average translational kinetic energy and thus the same temperature.
In summary, what is temperature? It is simply the human-scale “thermostat reading” of an assembly’s average translational kinetic energy. It summarizes trillions of microscopic energies into one single, easily readable number.
