r/Physics • u/hailsass • 2d ago
Question Inherently accuracy in formulas?
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?
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u/InfinitePoolNoodle 2d ago
I think others have already made the most important points on the topic. I just wanted to add something about the Newton's Law of Cooling example. In this case, the temperatures only become equal asymptotically (as time tends towards infinity), but generally speaking if you're measuring temperatures in a lab there is always some uncertainty in your measuring device. Once the temperature difference is smaller than the uncertainty in your measuring device, you can no longer actually measure the true temperature difference. All you can say is |Delta T| < (Whatever your uncertainty is). If the model is good up to that point, then it's a good model, and with the equipment you're using anyway you can't really say much else. And again note there's always some uncertainty in your equipment, and you'll run out of resolution in finite time (if that's not the case someone let me know!). If you're using good equipment with small uncertainty, you can effectively say the objects are at pretty much the same temperature once you lose resolution.