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I'm not a physicist, but I was having a discussion with a friend and I could not convince her about the main point.

I asked her: "If I am in a place which temperature is 10ºC and she is in a place which temperature is 20ºC, can I assert that the temperature where she is the DOUBLE of the temperature where I am?".

What I need is a mathematic/physic explanation answering yes or no, and why.

Thx.

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    $\begingroup$ The Celsius temperature scale is a difference scale, not a ratio scale. Try doubling $0^\circ$ C. $\endgroup$
    – David H
    Apr 18, 2014 at 18:08
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    $\begingroup$ 20 is indeed two times 10, so in that narrow sense you are right. However, physicists recognize the "absolute temperature scale" which starts at the coldest possible temperature, around -273 C. On that scale, the Kelvin scale, you are "wrong". So in order to stay friends, why don't you agree you are both right, and go have a (cold) beer. $\endgroup$
    – Floris
    Apr 18, 2014 at 18:18
  • $\begingroup$ @Leandro, But you can assert that she is in a place which is at a temperature $10^o$ higher than the place where you are, and yes it'd make 'sense'. $\endgroup$
    – Shubham
    Apr 18, 2014 at 18:26
  • $\begingroup$ I was told by someone that measurements in C and F use the degree symbol, but not K, because it doesn't follow vector space rules, but I can't find a source to back it up. $\endgroup$
    – Neil
    Nov 18, 2018 at 21:20

3 Answers 3

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If you want absolute temperatures, then the answer would be no. If you don't care about scales, but just numerical value, I'd say yes.

The Celcius scale is a 'relative' scale, based on the freezing and boiling points of water, and the temperatures in $^oC$ do not have much meaning. Whatever they tell, they only tell it with respect to freezing and boiling points of water.

The Kelvin scale, on the other hand is an absolute measure of temperature, and are better suited for comparisons. The equivalent temeratures for $10^oC $ and $20^oC$ in Kelvin scale are $283 K$ and $293 K$. The notion of 'double' temperature on Kelvin Scale would mean that the resulting temperature would have twice the effect (for a 'linear' relationship), whereas this is not the case for Celcius Temperatures.

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    $\begingroup$ I just want to add that the reason the Kelvin scale is a "good" scale is because its proportional to physical quantities such as thermal energy. That's why its a physical scale as opposed to a relative scale as the Celcius scale. $\endgroup$
    – JeffDror
    Apr 18, 2014 at 19:46
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Yes, you can assert it, and in one sense you are obviously correct - but only so long as you insist that Celsius is the "real" way to measure temperature.

10 degrees C is 50 degrees Fahrenheit. 20 degrees C is 68 degrees F. 68 / 50 is 1.36. So, are you claiming her to be simultaneously double the temperature AND 1.36 times the temperature?

Or, more fundamentally, exactly what do you mean by "double the temperature"? Think about Stubham's answer.

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Double of 10°C is 293.3°C

(First convert to Kelvins then double then convert back to Celsius.)

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    $\begingroup$ You forgot to change back to C: 10 C = 283 K; 283 K * 2 = 566 K = 293 C. $\endgroup$
    – Kyle Kanos
    Apr 21, 2015 at 12:50

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