Conservation of mass in the context of "Conservation law"

The law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time. In the case of a closed system, the principle says that the total amount of energy within the system can only be changed through energy entering or leaving the system. Energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another. For instance, chemical energy is converted to kinetic energy when a stick of dynamite explodes. If one adds up all forms of energy that were released in the explosion, such as the kinetic energy and potential energy of the pieces, as well as heat and sound, one will get the exact decrease of chemical energy in the combustion of the dynamite.

Classically, the conservation of energy was distinct from the conservation of mass. However, special relativity shows that mass is related to energy and vice versa by ${\displaystyle E=mc^{2}}$, the equation representing mass–energy equivalence, and science now takes the view that mass-energy as a whole is conserved. This implies that mass can be converted to energy, and vice versa. This is observed in the nuclear binding energy of atomic nuclei, where a mass defect is measured. It is believed that mass-energy equivalence becomes important in extreme physical conditions, such as those that likely existed in the universe very shortly after the Big Bang or when black holes emit Hawking radiation.

According to Jain doctrine, the universe and its constituents—soul, matter, space, time, and principles of motion—have always existed. Jainism does not support belief in a creator deity. All the constituents and actions are governed by universal natural laws. It is not possible to create matter out of nothing and hence the sum total of matter in the universe remains the same (similar to law of conservation of mass). Jain texts claim that the universe consists of jiva (life force or souls) and ajiva (lifeless objects). The soul of each living being is unique and uncreated and has existed during beginningless time.

The Jain theory of causation holds that a cause and its effect are always identical in nature and hence a conscious and immaterial entity like God cannot create a material entity like the universe. Furthermore, according to the Jain concept of divinity, any soul who destroys its karmas and desires achieves liberation (nirvana). A soul who destroys all its passions and desires has no desire to interfere in the working of the universe. Moral rewards and sufferings are not the work of a divine being, but a result of an innate moral order in the cosmos: a self-regulating mechanism whereby the individual reaps the fruits of their own actions through the workings of the karmas.

Mikhail Vasilyevich Lomonosov (/ˌlɒməˈnɒsɒf/; 19 November [O.S. 8 November] 1711 – 15 April [O.S. 4 April] 1765) was a Russian polymath, scientist and writer, who made important contributions to literature, education, and science. Among his discoveries were the atmosphere of Venus and the law of conservation of mass in chemical reactions. His spheres of science were natural science, chemistry, physics, mineralogy, history, art, philology, optical devices and others. The founder of modern geology, Lomonosov was also a poet and influenced the formation of the modern Russian literary language.

The Navier–Stokes equations (/nævˈjeɪ ˈstoʊks/ nav-YAY STOHKS) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician Sir George Gabriel Stokes, Bt. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842–1850 (Stokes).

The Navier–Stokes equations mathematically express momentum balance for Newtonian fluids and make use of conservation of mass. They are sometimes accompanied by an equation of state relating pressure, temperature and density. They arise from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing viscous flow. The difference between them and the closely related Euler equations is that Navier–Stokes equations take viscosity into account while the Euler equations model only inviscid flow. As a result, the Navier–Stokes are an elliptic equation and therefore have better analytic properties, at the expense of having less mathematical structure (e.g. they are never completely integrable).