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May 8th, 2017, 05:15 AM   #21
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Originally Posted by greg1313 View Post
The temperatures are akin to vectors in the sense that -4 is a vector in the negative x direction with a magnitude of 4. With that, 4 times hotter than -4 is 12 degrees C.
It depends on what "hotter" means. Below are some possible definitions:

1. If four times "hotter" means "temperature is four times higher" then the answer depends on the scale you use. If the scale is the Celsius scale, then 12 degrees C is four times hotter. If you use the Kelvin scale, you get 1076.6 K. You'll get a different result for Fahrenheit too. This is bad definition because different people using different scales get different answers.

2. If four times "hotter" means "a higher temperature such that heat exchanges between the object and something else is four times higher" then your answer depends on the temperature of the "something else" object. This definition is a lot more in line with how people sense how hot something is, but it can also give false positives (a classic example is touching a metal substance at room temperature... it feels cold even though the temperature difference is very small because metals are good conductors of heat). It also depends on the temperature of the "something else" object, which is not very good.

3. If four times hotter means "an object that has a higher temperature such that the internal energy content is four times higher", then you don't get a temperature which is four times higher, even on the Kelvin scale. This is because temperature is non-linear with internal energy at very low temperatures and because different substances exhibit different behaviours at threshold temperatures, such as change of phase, evaporation/sublimation, etc. However, if you can correctly assume for your problem that the increase in internal energy is linear with temperature (as is the case for ideal gases for example), then you can do an operation similar to part 1. with the Kelvin scale to get a new temperature.

4. If four times hotter means "an object that has an internal energy such that the temperature is four times higher" then the calculation is rather simple in terms of temperature using the Kelvin scale, but you might find that the material you have does not have an internal energy that is four times higher, it will be larger. However, if you can correctly assume for your problem that the increase in internal energy is linear with temperature (as is the case for ideal gases for example), then you can do an operation similar to part 1. with the Kelvin scale to get a new temperature.

Most physicists don't use "hotter" and "colder" as quantitative descriptors for this reason; they use it qualitatively to describe a comparison between two temperatures. Hence a better worded question would be

"A substance is at -4 degrees Celsius. Its temperature is increased by a factor of four in the <insert scale here> scale, making it hotter. What is the new temperature?"

Last edited by Benit13; May 8th, 2017 at 05:20 AM.
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May 8th, 2017, 07:22 AM   #22
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Originally Posted by romsek View Post
assuming a scale that had 0 at 0 kelvin you wouldn't need to convert to kelvin to do the computation.

This is what Archie mentioned a few posts back.
I agree, you can do the computation on any scale you like as long as 0 is absolute, and when it's converted back to whatever other scale you want, it will be the same as if you used kelvin during the calculation. You could use a similar scale to the celcius/kelvin conversion but for Fahrenheit, I think F goes to U as C goes to K (see what I did there )
Where 0U is -459.67F and 459.67U is 0F
You still end up with 803.45C because temperature is (as far as I'm aware) linear.
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May 8th, 2017, 06:43 PM   #23
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Originally Posted by greg1313 View Post
The temperatures are akin to vectors in the sense that -4 is a vector in the negative x direction with a magnitude of 4. With that, 4 times hotter than -4 is 12 degrees C.
Well, I'll choose this answer.
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May 8th, 2017, 11:27 PM   #24
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Originally Posted by Monox D. I-Fly View Post
Well, I'll choose this answer.
What if I asked, what's 4x hotter than -273.15 degC?
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