DeltaU=q+w

[Te Jung Yang 4K]

I don't understand why the equation is change in U is equal to q + w. Why is it not change in U is equal to the change in q + the change in w?

[Kyle Golden Dis 2G]

q and w inherently denote change because it is a transfer of energy.

[305113590]

Both q and w are considered to be change already. Since heat is flowing between the system and surroundings, there is already a change in heat being transferred/absorbed/released. Same applies for work. Work is a broad term, but it's the merely the idea that something is capable of doing stuff. When we look at the equation of -P∆V and -nRTln(V2/V1), there is an area under the curve that is indicative of work with infinitesimal changes. Both q and w already are going through changes, so it isn't necessary to write a delta.

[taryn_baldus2E]

The change in q and w can be assumed whereas internal energy is a state function.

[Joon Chang 2F]

q and w are both path functions and both represent transfers of energy between systems and their surroundings.

[Jchellis 1I]

Yes but q is energy lost as heat it does no work.