In most of the theories or derivations we take some assumptions like has is ideal, frictionless piston and many more but these are not applicable in real world. But in our real life situations we apply these conditions though the cases are not ideal. Why?
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$\begingroup$ Spherical cow. $\endgroup$– AccidentalFourierTransformCommented Aug 6, 2018 at 16:16
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$\begingroup$ Most maps depict the city I live in as perfectly flat. But this is not applicable in the real world, where there are hills. But in real life, people still use maps to navigate the city. Why?? $\endgroup$– WillOCommented Aug 6, 2018 at 17:17
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$\begingroup$ Ask yourself whether real life contains perfect geometric figures like circles, squares, triangles, trapazoids, spheres, cubes, etc. Why aren't you uncomfortable using these, even though they are not ideal? $\endgroup$– Chet MillerCommented Aug 6, 2018 at 20:04
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$\begingroup$ Essentially, if I'm not mistaken, your eventual question is "Why do we use approximations?" Seems like a strange question with several obvious enough answers... Looks like you had added the thermodynamics tag even before QMechanic's edit. it'd be great if you could expand a bit about the significance of that tag. $\endgroup$– user191954Commented Aug 17, 2018 at 3:39
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3 Answers
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Beacause the aim of physics is to build models that describe the reality, since the real world is too difficult to deal with . We know the exact solution just for a few physical system really simple to be treated, like the ideal harmonic oscillator, or perfect gas. The important thing is that although the real cases are pretty different from the ideal ones, you can still get excellent results with simple models based on the idealization of physical systems. Today, with numerical simulations, any analitical result can be improved by methods that add correction to a simple model, making the gap between physical modelization and reality smaller and smaller
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In applying these theories or concepts to real life problems we do so but by removing the many constraints we imposed in order to get the theory in the first place. In quite many real life problems the underlying theory helps us broadly understand what is going on and the additional constraints help us observe the transition from theory to a real life scenario. For eg :- when a stone is dropped we know that it falls down in accordance with the law of gravitation. But we also know in order to understand the motion at each point and instant we would also have to factor in things like drag resistance due to air, etc etc. But roughly to answer the question "Why does a stone fall down?" the answer "Due to gravity." should infact suffice.
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Firstly I would say that you are wrong in stating that we apply the ideal solutionsnto real world problems. It is almost impossible to get an analytic solution if we start off by trying to solve the real world problem. Instead, we assume a simpler model which is analytically solvable. When we have this solution, we next check how far off its results are from real values. Then we add various correction terms to it in order to get closer to a more realistic solution. This is much easier than trying to solve the much more difficult problem head on.
