Conservation of Mass

Conservation laws are the backbone of physics. They determine what can occur or what cannot occur. Some of them are considered to be universal in the sense that it is believed that any possible process has to fulfill them without exception. From the fundamental point of view, these conservation laws are either motional (the conservation of momentum, energy, linear momentum, etc..) or material (Conservation of charges). No one has observed any process violating any of these rules. 

However, we remark that the conservation laws are only necessary conditions and not at all sufficient conditions. A hypothetical process that obeys only these conditions is thus not necessarily a process that can really take place in nature. So in classical physics, a process that occurs in nature has to obey an additional condition: the conservation of matter in the form of the conservation of mass. The conservation of mass plays an important role in nature, in physics the conservation of mass is depicted with the help of consideration of conservation of electric charges. The concept of conservation of mass is widely used in the field of classical mechanics, chemistry, and fluid mechanics.

Law of Conservation of Mass:

The law of conservation of mass is formulated and systematized by 18th-century French chemist Antoine Lavoisier. According to the conservation of mass, all the reactions and interactions within a closed system will leave the mass of the system unchanged. In other words, the conservation of mass refers to the fact that the mass of an isolated system or closed system is neither increased nor decreased by the reaction between the parts. The total mass of the system before the reaction will be equal to the mass of the system after the reaction. The matter is always conserved.

What is The Law of Conservation of Mass:

The law of conservation of mass states that the matter can neither be created nor be destroyed, but it can be changed. It is also known as the conservation of matter. From the statement of the law of conservation of mass, it is understood that matter is conserved. In a closed system, the mass of all the substances before the chemical reaction will be the same as the mass of the substances after the chemical reactions.

According to the law of conservation of mass during any chemical reaction, no atoms will be created nor be destroyed, therefore the mass of reactants must be equal to the mass of the products in any low energy thermodynamic process. Initially, it is believed that the law of conservation of mass or the law of conservation of matter originated from classical mechanics, after some time it was modified according to quantum mechanics with the help of the mass-energy relation. In 1789, Antoine Laurent Lavoisier was an 18th-century French chemist who proposed the law of conservation of mass and discovered the conservation of mass. 

Derivation:

Though the conservation of mass mainly focused on the chemical reactions it’s considered to be equally important from the physics point of view as well. According to the conservation of mass, it says that the object or the collection of the object will remain the same no matter how many times we rearrange, it parts it away. With the help of the concept of the theory of relativity, the concept of mass underwent a radical revision. The meaning of mass lost its absoluteness. The mass of an object was seen to be equivalent to energy, and the mass and energy of the system were found to be interconvertible and to increase significantly at increasing high speeds near that of light. 

The meaning of the mass has been always varying according to the concerned subject of discussion. The mass has been viewed mainly in two compatible ways in physics. Sometimes the mass is viewed as a measure in terms of inertia, and sometimes as an opposition that offers forces to the body in motion. Thus, from the perspective of either inertial mass or the gravitational mass, according to the principle of the law of mass conservation, different measurements of the mass of an object considered under various circumstances should always be the same.

Consider a collection of objects located somewhere in space. This quantity of matter or the system of objects with well-defined boundaries is known as a system. The law of conservation of mass then implies that the mass of this given system remains constant it can not be created nor be destroyed, therefore, we get,

\[ \Rightarrow \frac{Dm}{Dt} = 0\]

Where, 

Dm is the infinitesimally small part of the considered system of objects. 

The volume occupied by the matter or the system of objects may be changing and the density of the objects within the system may be changing, but the mass of the system remains constant.

Importance of Conservation of Mass:

Physics is essentially an experimental and observational science. Predictions of any theory have to be confronted with experiments and observations. Conservation laws are the backbone of physics. All observed processes should conserve all universal laws and also specific laws associated with the interaction which governs the observed process.

The conservation of mass implies that matter can be neither created nor destroyed—i.e., processes that change the physical or chemical properties of substances within an isolated system or a closed system (such as the conversion of a liquid to a gas) leave the total mass unchanged. Strictly speaking, mass is not a conserved quantity. However, except in nuclear reactions, the conversion of rest mass into other forms of mass-energy is so small that, to a high degree of precision, rest mass may be thought of as conserved.

Did You Know:

The history associated with the discovery of the conservation of mass is remarkable. An important idea from ancient Greek philosophy was that "Nothing comes from nothing" so that what exists now has always existed: no new matter can come into existence where there was none before. An explicit statement of this, along with the further principle that nothing can pass away into nothing, is found in Empedocles (approx. 490–430 BC): "For it is impossible for anything to come to be from what is not, and it cannot be brought about or heard of that what it should be utterly destroyed." We knew about the conservation of mass from ages and it took centuries to frame it to a universal law.

Jain philosophy, a non-creationist philosophy based on the teachings of Mahavira (6th century BC), states that the universe and its constituents such as matter cannot be destroyed or created. The Jain text Tattvarthasutra (2nd century AD) states that a substance is permanent, but its modes are characterized by creation and destruction. A principle of the conservation of matter was also stated by Nasīr al-Dīn al-Tūsī (1201–1274). He wrote that "A body of matter cannot disappear completely. It only changes its form, condition, composition, color, and other properties and turns into a different complex or elementary matter".