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Everything around us consists of different substances. Ships and bathhouses are built from wood, irons and cots are made from iron, tires on wheels and erasers on pencils are made from rubber. And different objects have different weights - any of us can easily carry a juicy ripe melon from the market, but we will have to sweat over a weight of the same size.

Everyone remembers the famous joke: “Which is heavier? A kilogram of nails or a kilogram of fluff? We will no longer fall for this childish trick, we know that the weight of both will be the same, but the volume will be significantly different. So why is this happening? Why do different bodies and substances have different weights with the same size? Or vice versa, the same weight with different sizes? Obviously, there is some characteristic due to which substances are so different from each other. In physics, this characteristic is called the density of matter and is taught in the seventh grade.

Density of a substance: definition and formula

The definition of the density of a substance is as follows: density shows what the mass of a substance is in a unit of volume, for example, in one cubic meter. So, the density of water is 1000 kg/m3, and ice is 900 kg/m3, which is why ice is lighter and is on top of reservoirs in winter. That is, what does the density of matter show us in this case? An ice density of 900 kg/m3 means that an ice cube with sides of 1 meter weighs 900 kg. And the formula for determining the density of a substance is as follows: density = mass/volume. The quantities included in this expression are designated as follows: mass - m, volume of the body - V, and density is designated by the letter ρ (Greek letter “rho”). And the formula can be written as follows:

How to find the density of a substance

How to find or calculate the density of a substance? To do this you need to know body volume and body weight. That is, we measure the substance, weigh it, and then simply substitute the obtained data into the formula and find the value we need. And how the density of a substance is measured is clear from the formula. It is measured in kilograms per cubic meter. Sometimes they also use a value such as grams per cubic centimeter. Converting one value to another is very simple. 1 g = 0.001 kg, and 1 cm3 = 0.000001 m3. Accordingly, 1 g/(cm)^3 =1000kg/m^3. It should also be remembered that the density of a substance is different in different states of aggregation. That is, in solid, liquid or gaseous form. The density of solids is most often higher than the density of liquids and much higher than the density of gases. Perhaps a very useful exception for us is water, which, as we have already considered, weighs less in the solid state than in the liquid state. It is because of this strange feature of water that life is possible on Earth. Life on our planet, as we know, originated from the oceans. And if water behaved like all other substances, then the water in the seas and oceans would freeze through, the ice, being heavier than water, would sink to the bottom and lie there without melting. And only at the equator, in a small column of water, would life exist in the form of several species of bacteria. So we can say thank you to the water for our existence.

The study of the density of substances begins in a high school physics course. This concept is considered fundamental in the further presentation of the fundamentals of molecular kinetic theory in physics and chemistry courses. The purpose of studying the structure of matter and research methods can be assumed to be the formation of scientific ideas about the world.

Physics gives initial ideas about a unified picture of the world. Grade 7 studies the density of matter on the basis of the simplest ideas about research methods, practical application of physical concepts and formulas.

Physical research methods

As is known, observation and experiment are distinguished among the methods for studying natural phenomena. They teach how to observe natural phenomena in elementary school: they take simple measurements, and often keep a “Nature Calendar.” These forms of learning can lead a child to the need to study the world, compare observed phenomena, and identify cause-and-effect relationships.

However, only a fully conducted experiment will give the young researcher the tools to uncover the secrets of nature. The development of experimental and research skills is carried out in practical classes and during laboratory work.

Conducting an experiment in a physics course begins with definitions of such physical quantities as length, area, volume. In this case, a connection is established between mathematical (quite abstract for a child) and physical knowledge. Appealing to the child’s experience and considering facts known to him for a long time from a scientific point of view contributes to the formation of the necessary competence in him. The goal of learning in this case is the desire to independently comprehend new things.

Density Study

In accordance with the problem-based teaching method, at the beginning of the lesson you can ask the well-known riddle: “What is heavier: a kilogram of fluff or a kilogram of cast iron?” Of course, 11-12 year olds can easily answer the question they know. But turning to the essence of the issue, the ability to reveal its peculiarity, leads to the concept of density.

The density of a substance is the mass per unit volume. The table, usually given in textbooks or reference publications, allows you to evaluate the differences between substances, as well as the aggregate states of a substance. An indication of the difference in the physical properties of solids, liquids and gases, discussed earlier, an explanation of this difference not only in the structure and relative arrangement of particles, but also in the mathematical expression of the characteristics of matter, takes the study of physics to a different level.

A table of the density of substances allows you to consolidate knowledge about the physical meaning of the concept being studied. A child, giving an answer to the question: “What does the density of a certain substance mean?”, understands that this is the mass of 1 cm 3 (or 1 m 3) of the substance.

The issue of density units can be raised already at this stage. It is necessary to consider ways to convert units of measurement in different reference systems. This makes it possible to get rid of static thinking and accept other systems of calculation in other matters.

Determination of density

Naturally, the study of physics cannot be complete without solving problems. At this stage, calculation formulas are introduced. in 7th grade physics, this is probably the first physical relationship of quantities for the kids. Special attention is paid to it not only due to the study of the concepts of density, but also due to the fact of teaching methods for solving problems.

It is at this stage that an algorithm for solving a physical computational problem, an ideology for applying basic formulas, definitions, and laws are laid down. The teacher tries to teach the analysis of a problem, the method of searching for the unknown, and the peculiarities of using units of measurement by using such a relationship as the density formula in physics.

Example of problem solving

Example 1

Determine what substance a cube with a mass of 540 g and a volume of 0.2 dm 3 is made of.

ρ -? m = 540 g, V = 0.2 dm 3 = 200 cm 3

Analysis

Based on the question of the problem, we understand that a table of densities of solids will help us determine the material from which the cube is made.

Therefore, we determine the density of the substance. In the tables, this value is given in g/cm 3, so the volume from dm 3 is converted to cm 3.

Solution

By definition: ρ = m: V.

We are given: volume, mass. The density of a substance can be calculated:

ρ = 540 g: 200 cm 3 = 2.7 g/cm 3, which corresponds to aluminum.

Answer: The cube is made of aluminum.

Determination of other quantities

Using the formula for calculating density allows you to determine other physical quantities. Mass, volume, linear dimensions of bodies associated with volume are easily calculated in problems. Knowledge of mathematical formulas for determining the area and volume of geometric figures is used in problems, which helps explain the need to study mathematics.

Example 2

Determine the thickness of the copper layer with which a part with a surface area of ​​500 cm 2 is coated, if it is known that 5 g of copper were used for the coating.

h - ? S = 500 cm 2, m = 5 g, ρ = 8.92 g/cm 3.

Analysis

The substance density table allows you to determine the density of copper.

Let's use the formula for calculating density. This formula contains the volume of the substance, from which linear dimensions can be determined.

Solution

By definition: ρ = m: V, but this formula does not contain the desired value, so we use:

Substituting into the main formula, we get: ρ = m: Sh, from which:

Let's calculate: h = 5 g: (500 cm 2 x 8.92 g/cm 3) = 0.0011 cm = 11 microns.

Answer: the thickness of the copper layer is 11 microns.

Experimental determination of density

The experimental nature of physical science is demonstrated through laboratory experiments. At this stage, the skills of conducting experiments and explaining their results are acquired.

A practical task to determine the density of a substance includes:

• Determination of liquid density. At this stage, children who have previously used a graduated cylinder can easily determine the density of a liquid using the formula.
• Determination of the density of a solid body of regular shape. This task is also not in doubt, since similar calculation problems have already been considered and experience has been gained in measuring volumes based on the linear dimensions of bodies.
• Determination of the density of an irregularly shaped solid. When performing this task, we use the method of determining the volume of an irregularly shaped body using a beaker. It is worth recalling once again the features of this method: the ability of a solid to displace a liquid whose volume is equal to the volume of the body. The problem is then solved in the standard way.

Advanced tasks

You can complicate the task by asking the children to identify the substance from which the body is made. The table of density of substances used in this case allows us to draw attention to the need for the ability to work with reference information.

When solving experimental problems, students are required to have the necessary amount of knowledge in the field of use and conversion of units of measurement. This is often what causes the greatest number of errors and omissions. Perhaps more time should be allocated to this stage of studying physics; it allows you to compare knowledge and research experience.

Bulk Density

The study of pure matter is, of course, interesting, but how often are pure substances found? In everyday life we ​​encounter mixtures and alloys. How to be in this case? The concept of bulk density will prevent students from making the common mistake of using average densities of substances.

It is extremely necessary to clarify this issue; to give the opportunity to see and feel the difference between the density of a substance and the bulk density is worth it at the early stages. Understanding this difference is necessary in further study of physics.

This difference is extremely interesting in the case of Allowing a child to study bulk density depending on the compaction of the material and the size of individual particles (gravel, sand, etc.) during initial research activities.

Relative density of substances

Comparing the properties of various substances is quite interesting based on the relative density of a substance - one of such quantities.

Usually the relative density of a substance is determined in relation to distilled water. As the ratio of the density of a given substance to the density of the standard, this value is determined using a pycnometer. But this information is not used in a school science course; it is interesting for in-depth study (most often optional).

The Olympiad level of studying physics and chemistry may also touch upon the concept of “relative density of a substance with respect to hydrogen.” It is usually applied to gases. To determine the relative density of a gas, find the ratio of the molar mass of the gas under study to the use is not excluded.

A table is provided of the density of liquids at various temperatures and atmospheric pressure for the most common liquids. The density values ​​in the table correspond to the indicated temperatures; data interpolation is allowed.

Many substances are capable of being in a liquid state. Liquids are substances of various origins and compositions that have fluidity; they are capable of changing their shape under the influence of certain forces. The density of a liquid is the ratio of the mass of a liquid to the volume it occupies.

Let's look at examples of the density of some liquids. The first substance that comes to mind when you hear the word “liquid” is water. And this is not at all accidental, because water is the most common substance on the planet, and therefore it can be taken as an ideal.

Equal to 1000 kg/m 3 for distilled and 1030 kg/m 3 for sea water. Since this value is closely related to temperature, it is worth noting that this “ideal” value was obtained at +3.7°C. The density of boiling water will be slightly less - it is equal to 958.4 kg/m 3 at 100°C. When liquids are heated, their density usually decreases.

The density of water is similar in value to various food products. These are products such as: vinegar solution, wine, 20% cream and 30% sour cream. Some products turn out to be denser, for example, egg yolk - its density is 1042 kg/m3. The following are denser than water: pineapple juice - 1084 kg/m3, grape juice - up to 1361 kg/m3, orange juice - 1043 kg/m3, Coca-Cola and beer - 1030 kg/m3.

Many substances are less dense than water. For example, alcohols are much lighter than water. So the density is 789 kg/m3, butyl - 810 kg/m3, methyl - 793 kg/m3 (at 20°C). Certain types of fuel and oil have even lower density values: oil - 730-940 kg/m3, gasoline - 680-800 kg/m3. The density of kerosene is about 800 kg/m3, - 879 kg/m3, fuel oil - up to 990 kg/m3.

Low density indicators are characterized by such liquids as: turpentine 870 kg/m 3,

The bodies around us consist of various substances: iron, wood, rubber, etc. The mass of any body depends not only on its size, but also on the substance of which it consists. Bodies of the same volume, consisting of different substances, have different masses. For example, having weighed two cylinders made of different substances - aluminum and lead, we will see that the mass of the aluminum cylinder is less than the mass of the lead cylinder.

At the same time, bodies with the same masses, consisting of different substances, have different volumes. Thus, an iron bar weighing 1 ton occupies a volume of 0.13 m 3, and ice weighing 1 ton occupies a volume of 1.1 m 3. The volume of ice is almost 9 times greater than the volume of an iron bar. That is, different substances can have different densities.

It follows that bodies with the same volume, consisting of different substances, have different masses.

Density shows the mass of a substance taken in a certain volume. That is, if the mass of a body and its volume are known, the density can be determined. To find the density of a substance, you need to divide the mass of a body by its volume.

The density of the same substance in solid, liquid and gaseous states is different.

The densities of some solids, liquids and gases are given in tables.

Densities of some solids (at normal atmospheric pressure, t = 20 ° C).

Densities of some liquids (at normal atmospheric pressure t = 20 ° C).

How is it that bodies that occupy the same volume in space can have different masses? It's all about their density. We become familiar with this concept already in the 7th grade, in the first year of teaching physics at school. It is a basic physical concept that can open up MKT (molecular kinetic theory) for a person not only in a physics course, but also in chemistry. With its help, a person can characterize any substance, be it water, wood, lead or air.

Types of density

So, this is a scalar quantity that is equal to the ratio of the mass of the substance under study to its volume, that is, it can also be called specific gravity. It is denoted by the Greek letter “ρ” (read as “rho”), not to be confused with “p” - this letter is usually used to denote pressure.

How to find density in physics? Use the density formula: ρ = m/V

This value can be measured in g/l, g/m3 and in general in any units related to mass and volume. What is the SI unit of density? ρ = [kg/m3]. Conversion between these units is carried out through elementary mathematical operations. However, it is the SI unit of measurement that is more widely used.

In addition to the standard formula, used only for solids, there is also a formula for gas under normal conditions (n.s.).

ρ (gas) = ​​M/Vm

M is the molar mass of the gas [g/mol], Vm is the molar volume of the gas (under normal conditions this value is 22.4 l/mol).

To more fully define this concept, it is worth clarifying exactly what quantity is meant.

• The density of homogeneous bodies is precisely the ratio of the mass of a body to its volume.
• There is also the concept of “substance density,” that is, the density of a homogeneous or uniformly distributed inhomogeneous body consisting of this substance. This value is constant. There are tables (which you probably used in physics lessons) that contain values ​​​​for various solid, liquid and gaseous substances. So, this figure for water is 1000 kg/m3. Knowing this value and, for example, the volume of the bath, we can determine the mass of water that will fit in it by substituting the known values ​​into the above form.
• However, not all substances are homogeneous. For such people, the term “average body density” was created. To derive this value, it is necessary to find out the ρ of each component of a given substance separately and calculate the average value.

Porous and granular bodies, among other things, have:

• True density, which is determined without taking into account voids in the structure.
• Specific (apparent) density, which can be calculated by dividing the mass of a substance by the entire volume it occupies.

These two quantities are related to each other by the porosity coefficient - the ratio of the volume of voids (pores) to the total volume of the body under study.

The density of substances can depend on a number of factors, and some of them can simultaneously increase this value for some substances and decrease it for others. For example, at low temperatures this value usually increases, however, there are a number of substances whose density behaves anomalously in a certain temperature range. These substances include cast iron, water and bronze (an alloy of copper and tin).

For example, ρ of water has its highest value at a temperature of 4 °C, and then relative to this value it can change both during heating and cooling.

It is also worth saying that when a substance passes from one medium to another (solid-liquid-gaseous), that is, when the state of aggregation changes, ρ also changes its value and does so in jumps: it increases during the transition from gas to liquid and during crystallization of the liquid . However, there are a number of exceptions here too. For example, bismuth and silicon have little value in solidification. An interesting fact: when water crystallizes, that is, when it turns into ice, it also reduces its performance, and that is why ice does not sink in water.

How to easily calculate the density of various bodies

We will need the following equipment:

• Scales.
• Centimeter (measurement), if the body under study is in a solid state of aggregation.
• Volumetric flask, if the substance being tested is a liquid.

First, we measure the volume of the body under study using a centimeter or volumetric flask. In the case of liquid, we simply look at the existing scale and write down the result. For a cubic wooden beam, it will, accordingly, be equal to the side value raised to the third power. Having measured the volume, put the body under study on the scales and write down the mass value. Important! If you are examining a liquid, do not forget to take into account the mass of the vessel into which the substance being examined is poured. We substitute the experimentally obtained values ​​into the formula described above and calculate the desired indicator.

It must be said that this indicator for various gases is much more difficult to calculate without special instruments, therefore, if you need their values, it is better to use ready-made values ​​​​from the table of substance densities.

Also, special instruments are used to measure this value:

• The pycnometer shows the true density.
• The hydrometer is designed to measure this indicator in liquids.
• Kaczynski's drill and Seidelman's drill are devices with which soils are examined.
• A vibration density meter is used to measure a given quantity of liquid and various gases under pressure.