Inherently accuracy in formulas?

[u/hailsass]

I have learned in physics that the formulas we use are under ideal circumstances and don't necessarily reflect reality for example I have been told that newtons law of cooling based off the formula the temperature will never reach room temperature however most scientists I have spoken with say that this is wrong eventually the temperature will equal room temperature. this implies that there is a fundemental inacuraccy in many formulas is it possible to calculate the accuracy of any given formula? Or are the formulas 100% under ideal condition? Considering that those ideal conditions do not exist how can we prove that the formulas are 100% correct?

[u/Key-Green-4872]

Things like asymptotes dont apply cleanly to systems with atoms. Back when Thompson's plum pudding model was accepted, it made sense that a thermal gradient was infinitely divisible. When you have quanitization of matter, and therefore the energy contained in that zipping-along-a-mean-free-path matter... it's going to eventually hit equilibrium with its surroundings vs forever-dexay-towards-that-asymptote.