Path Functions

Path functions, like heat and work, have different values depending on what path is taken from the initial to the final state.
State functions, like the internal energy, do not depend on the path.

[@zulqarnainchaughtai]

Some people say that first law is more mysterious than 2nd law b/c sum of two inexact differentials give us exact differential i.e. internal energy. What are your thoughts?

[@PhysicalChemistry]

That's a fascinating question. It's only mysterious if you take the point of view that heat and work are more important. Then it seems like magic that their inexactness somehow cancels out when you add them together. That's a natural point of view because we came up with the concepts of heat and work quite early in the history of thermodynamics. Internal energy came later. Heat and work are often still taught first, so they seem more primary. But really, internal energy is the more primary quantity. Heat and work are just a particular partitioning of that energy. (See here for more details on why: kzbin.info/www/bejne/l5bOnKuljMmMd7M) Here's an analogy: Suppose I live in a hilly town. I want to go to the store, which happens to be at the same altitude as my house. I can take a lot of different routes to the store. I like to ride my skateboard on the downhill roads, but I walk on the uphill roads. I notice that -- no matter what route I take!! -- the altitude I climb on the walking sections is exactly the same as the altitude I coast down on the downhill sections. This is true despite the fact that every route I take involves a different amount of hills, so a different amount of skateboard time. This is mysterious if I think of skateboarding and walking as both being path functions. But not as mysterious if I remember that altitude is a state function.

[@zulqarnainchaughtai]

@@PhysicalChemistry Thank you