[AdiDex]

I struck with a question , I know work and heat are path function overall . But what if We apply some constrain , their behavior will also change .
I reached to the conclusion , Yes they can be state function in following conditions .

Work

at constant pressure
ΔU =  q  + w
ΔU = ΔH + w
w = ΔU - ΔH
since we can express it in the form of sum of two state function it is a state function .
 I visualized graphically it on PV diagram , if reversible process then there will be only one pathway to go from one state to another that is constant pressure path (horizontal line) .
Q.1 Can we visualize for irreversible change graphically  ??
Adiabatic condition

ΔU = w

So w must be state function.

but what about at constant volume .
w = 0 , no matter which path you will take, you always end with zero work .

Q.2 so can we say null function is also a state function ??

I also thought that it's differential will also be exact because you will get everytime 0 .

same question is with heat in a adiabatic process ??

[AdiDex]

I think what we think only does not matter at all in science . What Maths and experiments says ..!!  let's wait for any senior member

[mjc123]

U is a state function; its value is defined for a particular state. ΔU is not, it is the difference between the U values for 2 different states. Likewise w and q are not state functions, they are the difference between 2 states. They differ from ΔU in that this is path-independent (because it is a state function); they are not.
Consider the attached diagram. Consider the isovolumetric heating AB. What are ΔU, ΔH, q and w for this process?
What about the isothermal+isobaric path ACB? You will expect ΔU and ΔH to be the same as for AB, but what about q and w? Are they the same if the isothermal compression is reversible, or performed by a constant external pressure P2?
To answer Q1, I can't see physically how the horizontal path can be other than reversible. I think an irreversible change would have to deviate from this path, e.g. if you injected heat faster than the system could respond mechanically, the pressure would initially rise and then fall as it equilibrated to state B, as indicated by the red curve on top of the line CB. Can you see graphically that the integral of VdP over this path is non-zero? And since w = -int PdV and ΔH = ΔU + int PdV + int VdP, then w ≠ ΔU - ΔH.