CHEMISTRY COMMUNITY

Conceptually, I understand how the internal energy of a system is not dependent upon the path taken to get to that state.

But work and heat are not state functions, and so it's hard for me to wrap my head around two non-state functions being able to combine to make a state function.

The other state functions we use, like entropy and enthalpy, are state functions because their mathematical components are also state functions.

What makes U different? Do we just decide external to the math that it's a state variable and then just accept that without strict mathematical reasoning? Or is there actually something about adding work and heat that produces a state variable.

Two systems can transfer different amounts of heat and do different amounts of work and still arrive at the same deltaU.

I view state functions as part of the definition of a variable- what it represents. We just defined internal energy as the inner store of kinetic and potential energy of a system which only cares about the current or previous states and not the paths. So yes, it just has to do with the definition of the variable. I think it's best just to use the mnemonic to remember all the state functions.

Why is heat capacity a state function?

All heat capacities are state functions since it does not matter how the heat was added or how the temperature was changed; you will still arrive at the same final temperature.