Equation #4: Statistical definition of temperature
Hands down, this is kind of an advanced topic so if you are not familiar with it, that is okay.
The usual way we measure temperature is through a thermometer. We have an intuitive sense of the temperature for everyday objects. In high school, you learn that temperature is related to the kinetic energy of a system: KE = 3/2kT; 1/2kT for each “degree of freedom”. However, the definition of temperature gets more refined in statistical mechanics. Here, we define temperature (actually, reciprocal of temperature) as a measure of the rate of change of entropy with respect to the energy of a system(loosely speaking). Note that we are talking about the absolute temperature(Kelvin). Entropy is not just the state of disorder of a system, rather a measure of how many ways it can get disordered(and ordered).
Sounds confusing? I don’t blame you! You can learn more about entropy here:
For more clear and technical explanation, watch this:
For more equations, see Famous equations in Physics