### Why is delta U a state function?

Posted:

**Tue Feb 11, 2020 11:46 pm**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.

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.