“Temperature stems from the observation that if you bring physical objects (and liquids, gases, etc.) in contact with each other, heat (i.e., molecular kinetic energy) can flow between them. You can order all objects such that:
- If Object A is ordered higher than Object B, heat will flow from A to B.
- If Object A is ordered the same as Object B, they are in thermal equilibrium: No heat flows between them.
Now, the position in such an order can be naturally quantified with a number, i.e., you can assign numbers to objects such that:
- If Object A is ordered higher than Object B, i.e., heat will flow from A to B, then the number assigned to A is higher than the number assigned to B.
- If Object A is ordered the same as Object B, i.e., they are in thermal equilibrium, then they will have the same number.
> Mind that all of this does not impose how we actually scale temperature.
> How we scale temperature comes from practical applications such as thermal expansion being linear with temperature on small scales.
An absolute scale for temperature is determined (up to proportionality) by the maximal efficiency of a heat engine operating between two reservoirs: e = 1 - T2/T1.
This might seem like a practical application, but intellectually, it’s an important abstraction away from the properties of any particular system to a constraint on all possible physical systems. This was an important step on the historical path to a modern conception of entropy and the second law of thermodynamics [2].
Yes, but this still allows infinitely many "temperature" scales. I.e. take the current definition of temperature, and apply any nondecreasing function to it.
