After schoolchildren got acquainted with the concept of mass and volume of substances in physics, they study the important characteristic of any body, which is called density. The following article is devoted to this particular value. The questions of the physical meaning of density are revealed below. A density formula is also provided. The methods of its experimental measurement are described.
Density concept
We begin the article by directly writing the formula for the density of a substance. It has the following form:
Ο = m / V.
Here m is the mass of the body in question. It is expressed in kilograms in the SI system. 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 indicates 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 how much mass is contained in a unit volume. Using the value of Ο, it is possible to estimate the weight of which of the two bodies will be greater with equal volumes, or the volume of which of the two bodies will be larger with equal masses. For example, a tree is less dense than iron. Therefore, with equal volumes of these substances, the mass of iron will significantly exceed the same value for wood.
Concept of relative density
The very name of this quantity indicates that the studied quantity for one body will be considered relative to a similar characteristic for another. The formula for the relative density Ο r has the following form:
Ο r = Ο s / Ο 0 .
Where Ο s is the density of the measured material, Ο 0 is the density relative to which Ο r is measured. Obviously, Ο r is dimensionless. It shows how many times the measured substance is denser than the selected standard.
For liquids and solids, this value is selected as the standard Ο 0 for distilled water at a temperature of 4 o C. It is at this temperature that the water has a maximum density, which is convenient for calculations - 1000 kg / m 3 or 1 kg / l.
For gas systems, it is customary to use air density at atmospheric pressure and a temperature of 0 o C. as a standard.
Density versus pressure and temperature
The studied value is not constant for a particular body if its temperature or external pressure is changed. However, liquids and solids in many situations are incompressible, that is, their density remains constant when the pressure changes, as well as when the temperature changes.
The effect 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. Hence, the density increases. An obvious effect of pressure on the studied characteristic is observed in the case of gases.
Temperature has the opposite effect of pressure. With increasing temperature, the kinetic energy of the particles of matter 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 for gases, this effect is observed more distinctly than for liquids and solids. There is an exception to this rule - it is water. It was experimentally established that in the temperature range 0-4 o With its density increases with heating.
Homogeneous and heterogeneous bodies
The density formula written above corresponds to the so-called average Ο for the body under consideration. If you select a small volume in it, then the calculated value of Ο i can differ greatly from the previous value. This fact is associated with the presence of an inhomogeneous mass distribution over the volume. In this case, the density Ο i is called local.
Considering the issue of inhomogeneous 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 continuity of the medium is violated, which means that it makes no sense to use the characteristic of local density. It is known that almost the entire mass of an atom is concentrated in its core, whose radius is about 10 -13 meters. The density of the nucleus is estimated by a huge figure. This is 2.3 * 10 17 kg / m 3 .
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 body shape is very complex, then hydrostatic weighing will be a universal method for determining density. It is based on the use of Archimedean force. The essence of the method is simple. First, the body is 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:
Ο = Ο l * P 0 / (P 0 - P l ),
where P 0 , P l - body weight in air and in liquid. Accordingly, Ο l is the density of the liquid.
According to legend, the hydrostatic weighing method for determining density was first used by a philosopher from Syracuse Archimedes. 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 for its manufacture.