After the students got acquainted with the concept of mass and volume of substances in physics, they study an important characteristic of any body, which is called density. The article below is devoted to this value. The questions of the physical meaning of density are revealed below. The density formula is also given. Methods for its experimental measurement are described.
The concept of density
Let's start the article with a direct recording of the formula for the density of matter. It looks like this:
ρ=m / V.
Here m is the mass of the considered body. It is expressed in the SI system in kilograms. In tasks and in practice, you can also find other units of its measurement, for example, grams or tons.
The symbol V in the formula denotes the volume that characterizes the geometric parameters of the body. It is measured in SI in cubic meters, however, cubic kilometers, liters, milliliters, etc. are also used.
The density formula shows what mass of a substance is contained in a unitvolume. Using the value of ρ, one can estimate which of the two bodies will have a greater weight with equal volumes, or which of the two bodies will have a larger volume with equal masses. For example, wood is less dense than iron. Therefore, with equal volumes of these substances, the mass of iron will significantly exceed the same value for a tree.
The concept of relative density
The very name of this quantity indicates that the value under study for one body will be considered relative to a similar characteristic for another. The formula for relative density ρr looks like this:
ρr=ρs / ρ0.
Where ρs is the density of the measured material, ρ0 is the density against which the value ρr is measured . Obviously, ρr is dimensionless. It shows how many times the measured substance is denser than the selected standard.
For liquids and solids, as standard ρ0 choose this value for distilled water at a temperature of 4 oC. It is at this temperature that water has a maximum density, which is a convenient value for calculations - 1000 kg/m3 or 1 kg/l.
For gas systems, it is customary to use air density at atmospheric pressure and temperature 0 as standard oC.
Dependence of density on pressure and temperature
The studied value is not constant for a particular body,if you change its temperature or external pressure. However, liquids and solids are incompressible in many situations, meaning their density remains constant as pressure changes as well as temperature changes.
The influence of pressure is manifested as follows: when it increases, the average interatomic and intermolecular distances decrease, which increases the number of moles of a substance per unit volume. So the density is increasing. A clear influence of pressure on the characteristic under study is observed in the case of gases.
Temperature has the opposite effect of pressure. With an increase in temperature, the kinetic energy of matter particles increases, they begin to move more actively, which leads to an increase in the average distances between them. The latter fact leads to a decrease in density.
Again, this effect is more pronounced for gases than for liquids and solids. There is an exception to this rule - this is water. It has been experimentally established that in the temperature range 0-4 oС its density increases with heating.
Homogeneous and inhomogeneous bodies
The density formula written above corresponds to the so-called average ρ for the considered body. If we allocate some small volume in it, then the calculated value ρi can differ greatly from the previous value. This fact is connected with the presence of a non-uniform distribution of mass over volume. In this case, the densityρi is called local.
Considering the issue of non-uniform distribution of matter, it seems interesting to clarify one point. When we begin to consider an elementary volume close to atomic scales, the concept of medium continuity is violated, which means that it makes no sense to use the local density characteristic. It is known that almost the entire mass of an atom is concentrated in its nucleus, the radius of which is about 10-13 meters. The density of the core is estimated by a huge figure. This is 2, 31017 kg/m3.
Density measurement
It was shown above that in accordance with the formula, the density is equal to the ratio of mass to volume. This fact allows us to determine the specified characteristic by simply weighing the body and measuring its geometric parameters.
If the shape of the body is very complex, then the universal method for determining the density will be hydrostatic weighing. It is based on the use of Archimedean force. The essence of the method is simple. The body is first weighed in air and then in water. The difference in weight is used to calculate the unknown density. To do this, use the following formula:
ρ=ρl P0 / (P0 - P l),
where P0, Pl - body weight in air and liquid. Accordingly, ρl is the density of the liquid.
The method of hydrostatic weighing to determine the density, according to legend, was first used by a philosopher from SyracuseArchimedes. He was able, without violating the physical integrity of the crown, to determine that not only gold, but also other less dense metals were used to make it.
