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I'm currently reading about the Carnot cycle and its significance on the formulation of entropy (because I want to try to understand the concept better), but I can't seem to answer the following question:

  • Why are state functions important in physics? What does it mean, physically, that a certain variable is a state function? I know the definition of state function, but I can't figure out why it would be important at all.

In the aforementioned Carnot cycle, some variables that are state are internal energy and entropy. Apparently Rudolf Clausius felt the need to define a certain state function he discovered to be 'entropy', so it must have a reason.

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state functions are important because you can analyse the system at a specific moment of time if you know its configuration at that moment, it doesn't matter how the system got to the state it is in now, they also describe the equilibrium state of the system. its similar to the importance of conservative forces in classical mechanics.

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