Explain the state function 'enthalpy, H'. What is the relationship between `DeltaU and DeltaH`?

Explanation

The heat absorbed at constant volume is equal to change in the internal energy `DeltaU=q_(v).` But in the heat absorbed at constant pressure, a part of it increases the internal energy `DeltaU` and the remaining part is used in the expansion work done by the system. If the initial state is represented with a subscript 1 and the final state with a subscript 2. Then the above equation can be written as
`U_(2)-U_(1)=q_(p)-p(V_(2)-V_(1))`
or `q_(p)=(U_(2)+pV_(2))-(U_(1)+pV_(1))`
The value of `U+pV` is called enthalpy and represented by H. So enthalpy.
`H=U+pV`
`q_(p)=H_(2)-H_(1)=DeltaH`
Though 'q' is path function, H is a state function because it depends on `U_(1)p and V_(1)` all of which are state functions. Therefore `DeltaH` is independent of path.
The relation between `DeltaU and DeltaH` is `DeltaH=DeltaU+pDeltaV(becausepDeltaV=W)`