## Why is delta U a state function?

$\Delta U=q+w$

Payton Kammerer 2B
Posts: 49
Joined: Tue May 01, 2018 3:00 am

### Why is delta U a state function?

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.

Diana_Diep2I
Posts: 130
Joined: Sat Aug 17, 2019 12:17 am

### Re: Why is delta U a state function?

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

Dina Marchenko 2J
Posts: 54
Joined: Thu Jul 25, 2019 12:16 am

### Re: Why is delta U a state function?

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.

Angela Prince 1J
Posts: 102
Joined: Sat Aug 24, 2019 12:17 am

### Re: Why is delta U a state function?

Why is heat capacity a state function?

Ariel Davydov 1C
Posts: 110
Joined: Thu Jul 11, 2019 12:16 am
Been upvoted: 1 time

### Re: Why is delta U 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.