Incidentally, why is the degree immune to disappearance in division unlike all other units? That is, if I divide a distance (m) by a speed (m/s) I get a duration (s). From sheer memory, degree doesn't work like that. Any clue why?
We didn't really have a better word for units of temperature, as "Celsiuses" or "Farhenheits" didn't become a thing, so "degrees (of) Celsius" or "degrees (of) Fahrenheit" is kind of what we're left with. We could have chosen to say "degrees (of) kelvin", but we decided to go with "kelvins" (like "meters" or "seconds") instead. It's just a choice of language.
Temperature does have dimensionality, but it's weird because it's a bulk property of a particular material. If you consider two stars, you can add their masses, or their volumes, and the resulting values are meaningful. But you can't add their temperatures. You can't even average their temperatures meaningfully without knowing the relative sizes of the stars and a bunch of other information either.
That said, I can't think of a situation where degrees (of temperature?) would disappear in a mathematical operation. Can you give a specific example?
I regret that the decades that have elapsed since I studied physical chemistry & thermodynamics don’t permit me to make a proper answer, but if you want this to make sense I believe you should look many orders of magnitude smaller- Boltzman’s derivation of the ideal gas law from Newtonian mechanics using statistical methods.
Temperature is basically thermal density; it’s not really a fundamental unit. Chemical engineers use steam tables all the time to convert temperature to heat or other quantities.
I understand why one could say that, but I’d say it’s more misleading than helpful. (And the reason why is directly connected to the problem TFA discusses.)
Instead of temperature, let’s look at time first.
If you’re measuring the temporal extent of an event, then it absolutely makes sense to divide 30s by 15s or 6 days by 3 days and obtain a dimensionless 2: one thing takes twice as long as another, and the factor 2 that doesn’t depend on the choice of units, so it’s dimensionless.
Now consider dates. The year AD 2022 denotes (not very precisely) a point in time by specifiying its distance from a fixed reference in years; as another example, astronomers use the “Julian day”, which is a (possibly non-integer) number of days from a different reference point.
And you could technically divide AD 2022 by AD 1011—the ratio between the distances to the reference point is indeed a dimensionless 2, and if you counted days from it instead of years it’d still be the same. But it’s just not a very useful statement. And if you divide the Julian days instead, you’ll get a different number, because the reference point has moved 4712 years. So you can divide the time coordinates as long as the chosen origin stays in place, but you can’t really divide points in time.
Similarly, when you’re talking about differences in temperature, degrees work like any other unit, but temperatures themselves cannot be divided in the standard scales (without tying yourself to the scale): you’ll get the same result in Celsius and Réaumur (using the same origin) but a different result in Fahrenheit (using a different origin).
Of course, the silly part is that there is a natural origin for temperature, it’s just that the usual scales don’t use it. But then there’s a natural origin for time as well (and you’ll occasionally see it used in cosmology), it’s just that it’s metrologically inconvenient (being known only very approximately) in addition to being very far away.
(Library assignment: what defines a coordinate system on an affine line?)
It isn't because it is a relative scale, Rankine uses degrees and it is an absolute temperature scale just like Kelvin. The difference, I'd say, is that the Rankine scale didn't go though the SI standardization process.
There is nothing special with division, "degree Celsius" is the unit, you can't separate the "degree" from the "Celsius". You can measure a thermostat dial in degrees Celsius per degree (of angle). The resulting unit is just that, not "Celsius".
It's not. If you divide temperature by temperature (T/T) you get unitless value. But it doesn't make sense (what does it mean Kelvins per Kelvin?) Your mistake is to take a scalar value for temperature: 300 K / 2 = 150 K (T/scalar = T).
