Volume and mass are two physical quantities that are inherent in all bodies in liquid, solid and gaseous states. One of the frequent tasks in physics is the translation of the body volume into its mass. How to convert volume to mass is described in detail in this article.
Body volume
Before considering the question of how to translate volume into mass, one should deal with physical concepts.
Volume is the region of space that the body occupies in all three dimensions. This means that if the body has certain dimensions in only one (line) or only in two dimensions (plane), then its volume is zero. Volume is a scalar quantity; therefore, adding and subtracting volumes should be done in the same way as for scalar (non- vector) quantities.
If we talk about the nature of the existence of volume from a physical point of view, it should be noted that this phenomenon owes its existence to the so-called Pauli exclusion principle, according to which the arrangement of two particles in the same quantum state is impossible.
In the International SI system of units, the volume is usually measured in cubic meters (m 3 ), but in some cases other units of measure are used, for example, cubic centimeters, kilometers, etc. The volume of liquids is often measured in liters (l): 1 l = 10 - 3 m 3 = 1 dm 3 .
Mass concept
Before considering how to convert volume to mass, you should also become familiar with body weight.
Mass as a physical quantity is the amount of matter or matter and determines the inertial properties of bodies, that is, their ability to accelerate when they are affected by some non-zero external force. Mass, like volume, is a scalar quantity and is inherent in any object in the Universe. The mass in SI is measured in kilograms. One kilogram is such a body mass at which this body acquires an acceleration of 1 m / s 2 when a force of 1 newton acts on it.
Often the mass is confused with body weight. The latter is the force with which the body presses on the support. Knowing this force and the characteristics of the gravitational field in which the body is located, in particular the acceleration of gravity, we can calculate the mass.
The mass should not be confused with the amount of the substance, which in SI is described in units of mol. In fact, a mole is the number of particles of a substance; therefore, different bodies having the same number of particles (atoms, molecules) that form them generally have different masses.
Physical quantity density
Finally, before moving on to the question of how to convert volume to mass, we consider density — a value that directly relates to this question.
In such sciences as chemistry and physics, the density of a certain substance is understood to mean the amount of mass that is enclosed in a certain volume. Since volume and mass are scalar quantities, density is also a scalar. Usually, the density is denoted by the Greek letter ρ (po).
According to the above definition, it can be mathematically written: ρ = m / V, where m is the mass of the body in kilograms, V is the volume in cubic meters that this body occupies. This means that the density is measured in units of kg / m 3 .
Density of homogeneous and inhomogeneous bodies
The formula for determining the density given in the previous paragraph is valid if the substance in the body is distributed evenly. In such cases, they speak of a homogeneous or homogeneous body.
If the body is heterogeneous, then each of its microregions is characterized by its own density value. In such cases, to determine the average density value for the whole body, it is necessary to measure its value in each microscopic volume of the body, add the obtained results and divide by the number of measurements taken.
Note that the concept of density is considered defined up to spatial scales of the order of 10 -8 m. On atomic scales, the concept of density loses its meaning, which is associated with a certain atomic structure. So, an atom consisting of a nucleus and electron shells has a radius of the order of 10 -10 m, the size of the atomic nucleus is of the order of 10 -13 m, that is, the radius of the atom is greater than the radius of its nucleus of 1000! Almost the entire mass of the atom is concentrated in its small nucleus, which leads to huge nuclear densities, they are about 10 17 kg / m 3 , that is, if it were possible to obtain a substance that would consist only of atomic nuclei, then 1 m 3 of this substance would have would have a mass of 100,000 billion tons! Approximately such densities exist in the Universe in neutron stars and black holes.
How to convert volume to mass in physics?
Having become acquainted with the definition of all necessary quantities, we will directly turn to the answer to the question in the article. To translate the volume into mass, we use the definition of the density of matter: ρ = m / V. From this formula we express the mass, we get: m = ρ * V.
Thus, if the body volume and the density value of the substance of which this body consists are known, then it is enough to multiply these quantities to obtain the body mass, which is the answer to the question of how to convert the volume to mass. It should be remembered that before multiplying volume and density, it is necessary to bring them to the appropriate units of measurement, for example, to [m 3 ] and [kg / m 3 ], respectively.
On the contrary, to translate mass into volume, the formula will fit the following: V = m / ρ, that is, the mass of the body must be divided by its density.
The relationship between volume and mass for water
To translate the volume of water into mass, you should use the above formula. However, for pure water, the density value is 1000 kg / m 3, or 1 g / cm 3, or 1 kg / l. This means that volume to mass and vice versa is easy to translate for this substance, for this you only need to know the correspondence between the units of measurement of these physical quantities. For example, 2 liters of water have a mass of 2 kg, and 3.5 tons of water occupy a volume of 3.5 m 3 .
Note that a density of 1000 kg / m 3 is characteristic only of pure water. Any impurities and salts can significantly change this indicator, for example, the density of sea water is 1027 kg / m 3 , that is, sea water is 2.7% denser than fresh.