What is called the average body density. Determination of density

DEFINITION

Density is the amount of substance per unit volume of a body on average.

This amount can be determined in different ways. If we are talking about the number of particles, then we talk about the particle density. This value is denoted by the letter n. In SI it is measured in m -3. If we mean the mass of a substance, then enter the mass density. It is denoted by . In Si it is measured in kg/m3. Between and n there is a connection. So, if a body consists of particles of the same type, then

= m× n,

Where m- mass of one particle.

Mass density can be calculated using the formula:

This expression can be transformed so that the formula for mass in terms of volume and density is obtained:

Table 1. Densities of some substances.

Regardless of the degree of compression, the densities of liquid and solid bodies lie in a very narrow range of values ​​(Table 1). The densities of gases vary within very wide limits. The reason is that in both solids and liquids the particles are closely adjacent to each other. In these media, the distance between neighboring particles is on the order of 1 A and is comparable to the sizes of atoms and molecules. For this reason, solids and liquids have very low compressibility, which accounts for the small difference in their density. In gases the situation is different. The average distance between particles significantly exceeds their sizes. For example, for air near the Earth's surface it is 10 2 A. As a result, gases have high compressibility, and their density can vary over a very wide range.

Examples of problem solving

EXAMPLE 1

EXAMPLE 2

Let us place iron and aluminum cylinders of the same volume on the scales (Fig. 122). The balance of the scales has been disrupted. Why?

Rice. 122

In lab work, you measured body weight by comparing the weight of weights to your body weight. When the scales were in equilibrium, these masses were equal. Disequilibrium means that the masses of the bodies are not the same. The mass of the iron cylinder is greater than the mass of the aluminum cylinder. But the volumes of the cylinders are equal. This means that a unit volume (1 cm3 or 1 m3) of iron has a greater mass than aluminum.

The mass of a substance contained in a unit volume is called the density of the substance. To find density, you need to divide the mass of a substance by its volume. Density is denoted by the Greek letter ρ (rho). Then

density = mass/volume

ρ = m/V.

The SI unit of density is 1 kg/m3. The densities of various substances are determined experimentally and are presented in Table 1. Figure 123 shows the masses of substances known to you in a volume V = 1 m 3.

Rice. 123

Density of solids, liquids and gases
(at normal atmospheric pressure)

How do we understand that the density of water is ρ = 1000 kg/m3? The answer to this question follows from the formula. The mass of water in a volume V = 1 m 3 is equal to m = 1000 kg.

From the density formula, the mass of a substance

m = ρV.

Of two bodies of equal volume, the body with the greater density of matter has the greater mass.

Comparing the densities of iron ρ l = 7800 kg/m 3 and aluminum ρ al = 2700 kg/m 3, we understand why in the experiment (see Fig. 122) the mass of an iron cylinder turned out to be greater than the mass of an aluminum cylinder of the same volume.

If the volume of a body is measured in cm 3, then to determine the body mass it is convenient to use the density value ρ, expressed in g/cm 3.

The substance density formula ρ = m/V is used for homogeneous bodies, that is, for bodies consisting of one substance. These are bodies that do not have air cavities or do not contain impurities of other substances. The purity of the substance is judged by the measured density. Is there, for example, any cheap metal added inside a gold bar?

Think and answer

1. How would the balance of the scales change (see Fig. 122) if instead of an iron cylinder a wooden cylinder of the same volume were placed on a cup?
2. What is density?
3. Does the density of a substance depend on its volume? From the masses?
4. In what units is density measured?
5. How to move from the unit of density g/cm 3 to the unit of density kg/m 3?

Interesting to know!

As a rule, a substance in the solid state has a density greater than in the liquid state. The exception to this rule is ice and water, consisting of H 2 O molecules. The density of ice is ρ = 900 kg/m 3, the density of water? = 1000 kg/m3. The density of ice is less than the density of water, which indicates a less dense packing of molecules (i.e., greater distances between them) in the solid state of the substance (ice) than in the liquid state (water). In the future, you will encounter other very interesting anomalies (abnormalities) in the properties of water.

The average density of the Earth is approximately 5.5 g/cm 3 . This and other facts known to science allowed us to draw some conclusions about the structure of the Earth. The average thickness of the earth's crust is about 33 km. The earth's crust is composed primarily of soil and rocks. The average density of the earth's crust is 2.7 g/cm 3, and the density of the rocks lying directly under the earth's crust is 3.3 g/cm 3. But both of these values ​​are less than 5.5 g/cm 3, i.e. less than the average density of the Earth. It follows that the density of matter located in the depths of the globe is greater than the average density of the Earth. Scientists suggest that in the center of the Earth the density of the substance reaches 11.5 g/cm 3, that is, it approaches the density of lead.

The average density of human body tissue is 1036 kg/m3, the density of blood (at t = 20°C) is 1050 kg/m3.

Balsa wood has a low wood density (2 times less than cork). Rafts and lifebelts are made from it. In Cuba, the Eshinomena prickly hair tree grows, the wood of which has a density 25 times less than the density of water, i.e. ρ = 0.04 g/cm 3 . The snake tree has a very high wood density. A tree sinks in water like a stone.

Do it yourself at home

Measure the density of the soap. To do this, use a rectangular shaped bar of soap. Compare the density you measured with the values ​​obtained by your classmates. Are the resulting density values ​​equal? Why?

Interesting to know

Already during the life of the famous ancient Greek scientist Archimedes (Fig. 124), legends were formed about him, the reason for which was his inventions that amazed his contemporaries. One of the legends says that the Syracusan king Heron II asked the thinker to determine whether his crown was made of pure gold or whether the jeweler mixed a significant amount of silver into it. Of course, the crown had to remain intact. It was not difficult for Archimedes to determine the mass of the crown. Much more difficult was to accurately measure the volume of the crown in order to calculate the density of the metal from which it was cast and determine whether it was pure gold. The difficulty was that it was the wrong shape!

Rice. 124

One day, Archimedes, absorbed in thoughts about the crown, was taking a bath, where he came up with a brilliant idea. The volume of the crown can be determined by measuring the volume of water displaced by it (you are familiar with this method of measuring the volume of an irregularly shaped body). Having determined the volume of the crown and its mass, Archimedes calculated the density of the substance from which the jeweler made the crown.

As the legend goes, the density of the crown’s substance turned out to be less than the density of pure gold, and the dishonest jeweler was caught in deception.

Exercises

1. The density of copper is ρ m = 8.9 g/cm 3, and the density of aluminum is ρ al = 2700 kg/m 3. Which substance is more dense and by how many times?
2. Determine the mass of a concrete slab whose volume is V = 3.0 m 3.
3. What substance is a ball with volume V = 10 cm 3 made of if its mass m = 71 g?
4. Determine the mass of window glass whose length a = 1.5 m, height b = 80 cm and thickness c = 5.0 mm.
5. Total mass N = 7 identical sheets of roofing iron m = 490 kg. The size of each sheet is 1 x 1.5 m. Determine the thickness of the sheet.
6. Steel and aluminum cylinders have the same cross-sectional area and mass. Which cylinder has the greater height and by how much?

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/cm3, so the volume from dm3 is converted to cm3.

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.

Bodies made of different substances with the same volumes have different masses. For example, iron with a volume of 1 m3 has a mass of 7800 kg, and lead of the same volume has a mass of 13000 kg.

A physical quantity that shows the mass of a substance per unit volume (i.e., for example, in one cubic meter or one cubic centimeter) is called density substances.

To find out how to find the density of a given substance, consider the following example. It is known that an ice floe with a volume of 2 m 3 has a mass of 1800 kg. Then 1 m 3 of ice will have a mass that is 2 times less. Dividing 1800 kg by 2 m 3, we get 900 kg/m 3. This is the density of ice.

So, To determine the density of a substance, you need to divide the mass of the body by its volume: Let us denote the quantities included in this expression by letters:

m- body mass, V- body volume, ρ - body density ( ρ -Greek letter "rho").

Then the formula for calculating density can be written as follows: The SI unit of density is kilogram per cubic meter(1 kg/m3). In practice, the density of a substance is also expressed in grams per cubic centimeter (g/cm3). To establish the connection between these units, we take into account that

1 g = 0.001 kg, 1 cm 3 = 0.000001 m 3.

That's why The density of the same substance in solid, liquid and gaseous states is different. For example, the density of water is 1000 kg/m3, ice is 900 kg/m3, and water vapor (at 0 0 C and normal atmospheric pressure) is 0.59 kg/m3.

Table 3

Densities of some solids

Table 4

Densities of some liquids

Table 5

Densities of some gases

(The densities of bodies indicated in tables 3-5 are calculated at normal atmospheric pressure and at a temperature for gases of 0 0C, for liquids and solids at 20 0C.)

1. What does density show? 2. What needs to be done to determine the density of a substance, knowing the mass of the body and its volume? 3. What units of density do you know? How do they relate to each other? 4. Three cubes - made of marble, ice and brass - have the same volume. Which one has the most mass and which one has the least? 5. Two cubes - made of gold and silver - have the same mass. Which one has the larger volume? 6. Which of the cylinders shown in Figure 22 has greater density? 7. The mass of each of the bodies shown in Figure 23 is 1 ton. Which of them has less density?