How exactly do temperature scales work?
If my understanding is correct, the Celsius scale has two fixed points: (definitions of temperature irrespective of scale) 1. The freezing point of pure water at 1atm (labelled 0 C) 2. The boiling point of pure water at 1atm (labelled 100 C)
Note that 0 and 100 are completely random numbers.
All other values of temperature are only defined using distance on a thermometer. eg. 50 deg. C is exactly half-way between the marks of 0 and 100 on a thermometer. It doesn't necessarily have to be "half as hot" as 100 deg. C (what is half as hot anyway?)
Since the coefficient of expansion depends on temperature anyway, how do we justify these scales?
The Kelvin Scale is simply C-273.15, to ensure that all temperatures remain positive.
So, how does the RMS speed of gas molecules (which is independent of human-invented temperature scales) depend so 'cleanly' on our arbitrary temperature scales?