How does the law of conservation of energy relate to energy transformations?
Regarding this, is energy conserved in quantum mechanics?
In general, yes. The phenomenon described by the Heisenberg uncertainty principle allows a "temporary" non-conservation of energy. The larger the amount of "non conserved" energy, the less time possible that the energy can be non conserved.
Furthermore, why is the law of conservation of energy so important? Conservation of energy is just a way to balance the energy from one form to the other form. Since you know that Energy can not be created or destroyed, we use conservation of energy to balance our energy “cheque books”. It's important to do so in order to calulate how much we need to generate.
One may also ask, which equation states the law of conservation of energy?
In classical mechanics, conservation of mass and conversation of energy are considered to be two separate laws. However, in special relativity, matter may be converted into energy and vice versa, according to the famous equation E = mc2. Thus, it's more appropriate to say mass-energy is conserved.
How objects can conserve energy even when energy changes form?
As objects move around over time, the energy associated with them—e.g., kinetic, gravitational potential, heat—might change forms, but if energy is conserved, then the total will remain the same. Conservation of energy applies only to isolated systems.