The Celsius unit is arbitrarily defined, based on the boiling and freezing point of water. Is it a coincidence, then, that the SI unit of temperature Kelvin, which is used in all natural equations, has the same length as the Celsius unit?

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    $\begingroup$ There is also the Rankine scale, which has the same unit length as the Fahrenheit scale, but shifted down such that 0°R = 0K. $\endgroup$
    – Tim
    Jun 9 '19 at 9:36
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    $\begingroup$ @Tim So if we wanted to adopt the Rankine scale, the Boltzmann constant would have to be assigned a different value, right? $\endgroup$
    – Siddhartha
    Jun 9 '19 at 11:12
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    $\begingroup$ @Thomas : its value would effectively be the same, modulo the scaling factor into foot-pounds per degree Rankine. $\endgroup$ Jun 9 '19 at 11:20
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    $\begingroup$ @Tim - The Boltzmann constant has units of energy units / temperature unit. Change the units and the Boltzmann constant changes. Both the conventional units used in the USA and the metric system used almost everywhere else are arbitrary. The only difference is that one must use $F=kma$ in the US rather than the more familiar $F=ma$ used in the metric system. $\endgroup$ Jun 9 '19 at 11:43
  • $\begingroup$ @Tim As of 20 May 2019, the Boltzmann constant is assigned its present value. en.m.wikipedia.org/wiki/2019_redefinition_of_the_SI_base_units $\endgroup$
    – Siddhartha
    Jun 9 '19 at 11:48

Kelvin history

The kelvin unit was designed so that a change of $1\ \text{K}$ corresponds to a change of $1\ ^\circ\text{C}$. This makes sense because people were working in Celsius at the time. Kelvin just realized that the Celsius scale couldn't go down arbitrarily negative. It stopped at $-273.15\ ^\circ\text{C}$.

The idea was to then make a new scale, the Kelvin scale which has the same gradations as the Celsius scale (for compatibility with the existing scale) but with the property that $0\ \text{K}$ corresponds to this special $-273.15\ ^\circ\text{C}$ temperature. In other words, it is not a coincidence but rather the kelvin was historically defined so that the two scales had the same gradation.

There is a bit of confusion regarding the triple point of water ($273.16\ \text{K}$, or $0.01\ ^\circ\text{C}$) and the freezing point of water at standard pressure ($273.15\ \text{K}$ or $0.00\ ^\circ\text{C}$). Let me clarify.

The Celsius, or Centigrade, scale was historically defined as follows. $0\ ^\circ\text{C}$ was defined to be the temperature (measured by, for example, a mercury thermometer) at which water (at standard atmospheric pressure: $101\,325\ \text{Pa}$) freezes. $100\ ^\circ\text{C}$ was chosen to be the temperature (at standard pressure) at which water boiled. Thus one degree Celsius is a gradation of temperature (as measured by a mercury thermometer, for example) equivalent $\frac{1}{100}$ of the temperature difference between the freezing and boiling points of water at standard pressure.

As early as the $17^{\text{th}}$ century scientists began to understand that the Celsius scale didn't go infinitely negative. In fact, the value where the Celsius scale would stop could be calculated and measured and it was found to occur at around $-273\ ^\circ\text{C}$. It seems to me that further refinement of laboratory experiments found the temperature to be $-273.15\ ^\circ\text{C}$. That is if you started at the freezing point of water $(0\ ^\circ\text{C})$, and went down by $273.15$ of the gradations described above, you would hit absolute zero.

Ok, we still haven't rigorously defined the kelvin. In 1967 people wanted to give good definitions to the units. The freezing point of water was a bad physical reference point because it depended on the water being at atmospheric pressure. But pressure varies with the weather and elevation on Earth so different labs might calibrate their thermometers differently by this metric. However, the temperature of the triple point of water is unambiguous (at least regarding pressure) because it only occurs when the pressure is at the right value. The triple point of water occurs at $0.01\ ^\circ\text{C}$. Thus, in 1967 it was resolved to define the kelvin as $\frac{1}{273.16}$ of the temperature of the triple point of water. This sets 1) $0\ \text{K}$ to be absolute zero as desired, 2) ensures the gradations of Kelvin were referred to a decent physical reference quantity and 3) has the effect that gradations of the Kelvin scale are the exact same as gradations of the Celsius scale.

I will leave the answer here for now. See A Peruzzi 2018 J. Phys.: Conf. Ser. 1065 12011: On the redefinition of the kelvin for details on the redefinition of the kelvin which went into effect last month.

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    $\begingroup$ One could add, that the starting point of the scale does not matter much in many applications, but temperature differences do matter. And preserving this numerical value is helpful, hence the same unit size. $\endgroup$
    – Chieron
    Jun 9 '19 at 10:18
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    $\begingroup$ Upvoted, but kelvin as a unit should be lowercase. Kelvin as a person is of course uppercase. $\endgroup$ Jun 9 '19 at 11:46
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    $\begingroup$ Isn't it $-273.15$? $\endgroup$
    – Wojowu
    Jun 9 '19 at 12:40
  • $\begingroup$ @Wojowu 273.15K is where water freezes = 0 degrees C, 273.16K is the triple point of water, which is the point that defines the Celcius scale $\endgroup$
    – Neil_UK
    Jun 9 '19 at 15:09
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    $\begingroup$ "people were working in Celsius at the time" most people are still working with the Celsius scale for measuring temperature, Kelvin is only used in specific areas of physics. $\endgroup$
    – user000001
    Jun 10 '19 at 5:56

Kelvins aren't really all that natural either; or rather, they are just as arbitrary as Celsius. You need another arbitrary quantity--the Boltzmann constant--to get the temperature unit to work with the other physical units.

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    $\begingroup$ Yes, exactly. The "zero point" of Kelvin is natural, but the scale is not. $\endgroup$
    – Noldorin
    Jun 9 '19 at 15:18

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