Internal energy ($U$ or $E$) is a state function, meaning its value is determined solely by the current state of the system and is independent of the path taken to reach that state . When a system moves from state A to state B, the change in internal energy is $E_{1} = U_{B} - U_{A}$. When the system returns from state B to state A, the change is $E_{2} = U_{A} - U_{B}$. Summing these changes for the entire cycle (A → B → A) gives $E_{1} + E_{2} = (U_{B} - U_{A}) + (U_{A} - U_{B}) = 0$ . This demonstrates that for any cyclic process, the net change in a state function is zero.