Conservation of energy


August 19, 2022

In physics and chemistry, the law of conservation of energy states that, in any isolated system, the total amount of energy is conserved. This law, first proposed and proven by Émilie du Châtelet, means that energy it cannot be created or destroyed; rather, it can only be transformed or transferred from one form to another. For example, chemical energy is converted to kinetic energy when a stick of dynamite explodes. If you add up all the forms of energy released in the explosion, such as the kinetic energy and potential energy of the pieces, as well as heat and sound, you will get the exact decrease in chemical energy in the combustion of dynamite. In the classical sense, conservation of energy was different from conservation of mass, but special relativity showed that mass is related to energy and vice versa by E mc ². This is why science now considers that mass-energy is generally conserved. Theoretically, this implies that any object with mass can be converted into pure energy and vice versa, although this is thought to be possible only under the most extreme physical conditions, such as probably existed in the universe shortly after the Big Bang or when black holes emit Hawking radiation. Noether's Theorem can rigorously demonstrate the conservation of energy as a consequence of the symmetry of the continuous function, that is, from the fact that the laws of physics do not change over time. A consequence of the law of conservation of energy is that a perpetual motion machine of the first type cannot exist, that is, no system without an external supply of energy can supply an unlimited amount of energy to its surroundings . For systems that do not have time-translational symmetry, it may not be possible to define conservation of energy. Examples include curved spacetimes in general relativity or time crystals in condensed matter physics.


In ancient times philosophers like Thales of Miletus had the intuition of the conservation of some kind of substance from which everything was made. But we have no reason to equate this with what we know today as mass-energy, in fact Thales thought it must be water. In 1638, Galileo published in Leiden Discorsi e Dimostrazioni Matematiche, intorno a due nuove scienze which includes the famous interrupted pendulum problem, which in modern parlance could be described as the conservative conversion of potential energy into kinetic energy and vice versa. However, Galileo did not establish the process as it is known today and neither can he be attributed with the knowledge of the essential principle. The first to attempt a mathematical formulation of the type of energy that is related to motion, kinetic energy, was Gottfried Wilhelm Leibniz between 1676 and 1689. Leibniz realized that in many mechanical systems of various masses each with a velocity wine, the relationship ∑ i m i v i 2 {\displaystyle \sum _{i}m_{i}v_{i}^{2}} it was preserved while the masses did not interact. He called this quantity the vis viva (living force) of the system. The principle represented the careful expression of an approximation to the conservation of kinetic energy in the absence of friction. Many physicists at the time thought that the conservation of momentum, even in systems with friction, defined by the momentum ∑ i m i v