Question

q(heat) and w(work) both are path functions, then why "Delta U" is a state function ? In fact Delta U= q+w !!

Answer 1

Answer:

Explanation:

Let us assume that the internal energy of system is U₁  at a point A and it follows a path 1 due to which its internal energy changes to U₂ at B.

Now if the system returns to point A by following a path 2 then the change in energy 1 and 2 must me the same and the internal energy at A should be U₁

because if it doesn't then it will contradict the first law of thermodynamics

which states that Energy can neither be created nor destroyed.

This means that Internal energy depends only on the state and not on the path

Answer 2

First of all you need to be very clear about state function and path function... See this figure to get an idea ✔️.

Delta U is a Differential value so it doesn't talk about area as Differential value talk about slope only...

Let U be the Initial Internal Energy and U' be the Final Internal Energy....

so U' = U + w + q ...

U' - U = w + q ...

Delta U = w + q (delta indicates change)

Hope it helps you