"Internal energy is a state function." Explain.

Explanation

If some mechanical work of about 1 kJ is carried by rotating a set of small paddles and thereby churning water, heat is produced. Thus the temperature increases. The new state of system B may have temperature `T_(b)`. This state of system from a state A at a temperature `T_(A)`. If the internal energy of system in the state A is `U_(A)` and in the state B is `U_(B)` the change in internal energy `DeltaU=U_(B)-U_(A)`.
In another way the system in the state A can be brought to the state B by dipping a hot rod into water which supply same amount of energy 1 kJ. Then we find the change in temperature is same in the first case say `T_(B)-T_(A)`.
This show that a given amount of work done irrespective of path produced the same change of state.
The internal energy U is characteristic of the state of the system. The adiabatic work `W_(ad)` required to bring about a change of state is equal to the difference between the value of U in one state and that in another state `DeltaU.`
`DeltaU=U_(2)-U_(1)=W_(ad)`
Therefore internal energy U of the system is a state function.