# Why is a degree Celsius exactly the same as a Kelvin?

How on earth is it possible that the difference between two temperatures in Celsius and Kelvin is exactly the same. Given the historical definition of Celsius, I find it hard to believe that this is pure coincidence.

• because it's defined like that.No better answer can be given. – ABC May 25 '13 at 11:43

## 2 Answers

It's because the Kelvin scale was and still is defined so that as a measure of temperature difference, one kelvin exactly coincides with one Celsius degree. So the temperature in kelvins was defined as the temperature in Celsius degrees minus $A$ where $A=273.15$ °C is the temperature of the absolute zero, without any additional multiplicative factor.

When people learned how to measure the temperature more accurately, they could have redefined the scales a little bit so that the new definition didn't depend on arbitrary constructs such as "ordinary atmospheric pressure" (which had to be imposed to define the boiling and freezing points previously). Today, one kelvin is defined so that the triple point of water is exactly 273.16 kelvins and the scale is "linear" in the usual sense (e.g. when one measures the pressure times volume of the ideal gas; absolute zero is 0 K, of course). But this is just a refinement that was designed to match, within the error margins, the previous definition based on the freezing and boiling points of water at reasonable pressures.

• Given your current phrasing, the minus sign in the definition of $A$ is incorrect. Just a minor remark. – Wouter May 25 '13 at 11:05
• Thanks. I was a bit confused given the fact that the Kelvin scale corresponds to the thermal energy of a gas (or E is proportional to T). I wrongly assumed that would also define 1 K. I now realize that that is not the case. If a different size were used, it would still be linear. – dexter May 25 '13 at 11:15
• Is -273.15 a exact number or does it have any impresicion? – jinawee May 25 '13 at 15:36
• The triple point of (Vienna Standard Mean Ocean) water is exactly 273.16 K. The freezing point of water is approximately 273.15 K (that number is correct to within 0.001 K). – Taymon May 25 '13 at 22:21
• Dear Jinawee, it's just how water works: water is a specific substance and at atmospheric pressure, the ratio of the absolute temperatures of its boiling point and its freezing point is 373.15/273.15. People haven't invented it, it's a fact of Nature that may be measured, and a very hard number to calculate theoretically because water is a messy molecule and a high number of the nearby molecules makes things even more messy. In the old definition, 273.15 was exact for the freezing point. Today, we use the convention that 273.16 is exact for the triple point, I wrote that already! – Luboš Motl May 26 '13 at 4:15

Wikipedia says:

The kelvin is defined as the fraction 1⁄273.16 of the thermodynamic temperature of the triple point of water (exactly 0.01 °C or 32.018 °F).

And:

1848

Lord Kelvin (William Thomson), wrote in his paper, On an Absolute Thermometric Scale, of the need for a scale whereby "infinite cold" (absolute zero) was the scale's null point, and which used the degree Celsius for its unit increment.

This is the historical data, so yes, I wouldn't say that this is a coincidence...

• Quite right ;-) See my response above.. Thanks all! – dexter May 25 '13 at 11:18
• @dexter Can you accept this correct answer which gives both the current dependency of the Kelvin on the degree celsius, as well as the historic one? – Kaz May 25 '13 at 16:03
• To me both answers are correct – dexter May 26 '13 at 12:50
• unfortunately, both cant be marked correct..! – Saurabh Raje May 26 '13 at 13:55
• I think the wikipedia article is more than sufficient to give the proper reason. – Saurabh Raje Jul 2 '13 at 6:26