In Randall T. Knight’s textbook “Physics for Scientists and Engineers” in the first chapter on thermodynamics (Ch. 16: A Macroscopic Description of Matter) one of the first conceptual questions is stated like so:
The sample in an experiment is initially at $t_1$°C. If the sample’s temperature is doubled, what is the new temperature in °C?
The answer to that implies the reference to absolute temperature (for simplicity, to one significant figure, as the book required), i. e.:
$t_2°C = (T_1 × 2)K - 273 = (t_1°C + 273) × 2 - 273$.
I understand that the whole idea of this question to reiterate to the pupil that we ought to think of temperature as a specific physical property, and not in an everyday sense, but I am confused about the wording. In the section on temperature author writes:
We will begin with the commonsense idea that temperature is a measure of how “hot” or “cold” a system is. These are properties that we can judge without needing an elaborate theory. As we develop these ieas, we’ll find that temperature T is related to a system’s thermal energy. […] We’ll study temperature more carefully in Chapter 18 and replace these vague notions of hot and cold with a precise relationship between temperature and thermal energy.
That is, as yet we are still at the stage of “vague notions”. Few paragraphs later Knight introduces Kelvin scale but nowhere there or in between does he specifically insists on that idea I mentioned after the formula. At least not that I can see.
Am I missing something that should be obvious to me, and I fail to grasp it instantly because my brain is depleted by 50+ hours a week of studies? Am I just plain stupid, because to my eternal shame it took me way too long to figure it out? Or was there a better way to home onto that idea by an author: what do other textbooks say on that topic, how do they word this concept? Is the question logically flawed or confusing, or is it the common way of describing the situation in scientific literature?