How is the principle of the conservation of energy stated?

The principle of conservation of energy is fundamentally stated as that energy cannot be created or destroyed in an isolated system; instead, it transforms from one form to another while the total energy remains constant. Therefore, when we say "energy in equals energy out," we are referring to the notion that the total amount of energy entering a system must equal the total amount of energy leaving that system, minus any changes within it. This statement encapsulates the essence of the conservation principle in practical contexts, such as in mechanical, electrical, and thermodynamic systems.

In contrast, the other statements misrepresent the principle: energy is not lost over time but change forms or is transferred; the claim that energy can be created and destroyed violates the core concept of conservation; and while energy can change form (like thermal to mechanical energy), stating that it cannot change form is inaccurate. Therefore, emphasizing the equality of energy in and out is a correct, precise depiction of this fundamental principle.