The study of the density of substances begins in the course of high school physics. This concept is considered fundamental in the further presentation of the foundations of molecular kinetic theory in the courses of physics and chemistry. The purpose of studying the structure of matter, research methods can be assumed to be the formation of scientific ideas about the world.
The initial ideas about a single picture of the world are given by physics. Grade 7 studies the density of matter on the basis of the simplest ideas about research methods, the practical application of physical concepts and formulas.
Methods of physical research
As you know, among the methods of studying natural phenomena, observation and experiment are distinguished. Observations of natural phenomena are taught in elementary school: simple measurements are taken, often they keep a “Calendar of Nature”. These forms of learning can lead the child to the need to explore 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 reveal the secrets of nature. The development of experimental, research skills is carried out in practical classes and in the course of laboratory work.
Conducting an experiment in a physics course begins with the definitions of such physical quantities as length, area, volume. At the same time, a connection is established between mathematical (quite abstract for a child) and physical knowledge. Appeal to the experience of the child, consideration of 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 purpose of training in this case is the desire for independent comprehension of the new.
Density study
In accordance with the problematic teaching method, at the beginning of the lesson, you can ask a well-known riddle: “Which is heavier: a kilogram of down or a kilogram of cast iron?” Of course, 11-12-year-olds can easily answer a question they know. But the appeal to the essence of the issue, the opportunity to reveal its peculiarity, leads to the concept of density.
The density of a substance is the mass of a unit of its volume. The table, usually given in textbooks or reference books, 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 mutual arrangement of particles, but also in the mathematical expression of the characteristics of a substance, takes the study of physics to a different level.
To consolidate knowledge about the physical meaning of the concept under study allows the density table of substances. The child, giving an answer to the question: “What does the value of 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 question of density units can be raised already at this stage. It is necessary to consider ways of converting units of measurement in different reference systems. This makes it possible to get rid of static thinking, to accept other systems of calculus in other matters.
Density determination
Naturally, the study of physics cannot be complete without solving problems. At this stage, calculation formulas are entered. in physics of the 7th grade, probably the first physical ratio of quantities for children. It is given special attention 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 the algorithm for solving a physical computational problem is laid, the ideology of applying the basic formulas, definitions, and patterns. The teacher is trying to teach the analysis of the problem, the method of searching for the unknown, 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 \u003d 540 g, V \u003d 0.2 dm 3 \u003d 200 cm 3
Analysis
Based on the question of the problem, we understand that the table of solids densities will help us determine the material from which the cube is made.
Therefore, we define the density of matter. In the tables, this value is given in g / cm 3, so the volume from dm 3 is converted to cm 3.
Decision
By definition: ρ = m: V.
We are given: volume, mass. The density of a substance can be calculated:
ρ \u003d 540 g: 200 cm 3 \u003d 2.7 g / cm 3, which corresponds to aluminum.
Answer: The cube is made of aluminum.
Definition of other quantities
Using the density calculation formula allows you to determine other physical quantities. Mass, volume, linear dimensions of bodies associated with volume are easily calculated in tasks. Knowledge of mathematical formulas for determining the area and volume of geometric shapes is used in tasks, which makes it possible to explain the need to study mathematics.
Example 2
Determine the thickness of the copper layer that covers a part with a surface area of 500 cm 2 if it is known that 5 g of copper has been used for the coating.
h-? S \u003d 500 cm 2, m \u003d 5 g, ρ \u003d 8.92 g / cm 3.
Analysis
The density table of substances allows you to determine the density of copper.
Let's use the density calculation formula. In this formula, there is a volume of a substance, based on which linear dimensions can be determined.
Decision
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, whence:
Let's calculate: h \u003d 5 g: (500 cm 2 x 8.92 g / cm 3) \u003d 0.0011 cm \u003d 11 microns.
Answer: copper layer thickness is 11 µm.
Experimental determination of density
The experimental nature of physical science is demonstrated in the course of laboratory experiments. At this stage, the skills of conducting an experiment, explaining its results are acquired.
A practical task for determining the density of a substance includes:
- Determination of the density of a liquid. At this stage, the guys who have already used a measuring cylinder before can easily determine the density of a liquid using a formula.
- Determination of the density of the substance of a solid body of regular shape. This task is also beyond doubt, since similar computational problems have already been considered and experience has been gained in measuring volumes by the linear dimensions of bodies.
- Determination of the density of an irregularly shaped solid body. When performing this task, we use the method of determining the volume of an irregularly shaped body using a beaker. It is useful to recall once again the features of this method: the ability of a solid body to displace a liquid whose volume is equal to the volume of the body. Further, the task is resolved in the standard way.
Tasks of increased complexity
You can complicate the task by inviting the children to determine the substance from which the body is made. The density table of substances used in this case allows you to pay attention to the need to be able to work with reference information.
When solving experimental problems, students are required to have the necessary amount of knowledge in the field of using and converting units of measurement. Often this is what causes the greatest number of errors and shortcomings. Perhaps this stage of the study of physics should be given more time, it allows you to compare the knowledge and experience of the study.
Bulk density
The study of a pure substance 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 not allow students to make a typical mistake and use the average values of the density of substances.
It is extremely necessary to clarify this issue, to give an opportunity to see, to feel the difference between the density of a substance and the bulk density is at an early stage. Understanding this difference is necessary in the further study of physics.
This difference is extremely interesting in the case. It is possible to allow the child to study the bulk density depending on the compaction of the material, the size of individual particles (gravel, sand, etc.) during the initial research activity.
Relative density of substances
Comparison of the properties of various substances is quite interesting on the basis of the relative density of a substance - one of these 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 a standard, this value is determined using a pycnometer. But this information is not used in the school course of natural science, it is interesting for deep study (most often optional).
The Olympiad level of studying physics and chemistry can also be affected by 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, the ratio of the molar mass of the test gas to the use is not excluded.
One of the most important controlled indicators in the production of cosmetics and the production of dietary supplements is density. Depending on the product being produced, the company's specialists " KorolevPharm» use several concepts and definitions of density.
A clearer definition of the concept of density requires clarification of the wording of this term:
With such a limit transition, it is necessary to take into account that at the atomic level any body is inhomogeneous, and therefore it is necessary to dwell on the volume that is used for the corresponding physical model used.
- Bulk density - under the bulk density of various bulk materials (sugar, lactose, starch, etc.) is understood the amount of this powder (bulk product), which is in a freely filled state in a certain unit of volume.
- Relative density - is the ratio of two concepts, i.e. terms, and can be considered as the ratio of volumetric, that is, bulk density, to true density.
Product density is an important parameter in the manufacture of cosmetic products, as it affects the appearance of the product, its organoleptic properties, weight and cost of the finished product. It is very important to take into account the density of the product when packing manufactured products into bottles, tubes, jars, and so on.
For example, the density of creams is less than one. As a rule, the density of the cream is in the range of 0.96 - 0.98 g / cm 3. In accordance with the tests carried out, at a density of 0.96 and a volume of 50 ml, the mass of the cream will be 48 g, and at a density of 0.98, the mass increases to 49 g.
The density of shampoos, on the contrary, is greater than or equal to one, it is in the range of 1.0 - 1.04 g/cm 3 . Studies show that with a density of 1.0 and a volume of 100 ml, the mass of the shampoo in the package will be 100 g, and with a density of 1.04 already 104 g.
As already mentioned, density is defined as the ratio of body mass to the volume occupied. Therefore, the numerical values of the density of a substance indicate the mass of the accepted or indicated unit volume of this substance. As can be seen from the above example, the density of the metal, in this case cast iron, is 7 kg / dm 3. It turns out that 1 dm 3 of cast iron has a mass of 7 kg. Compare the density of tap water - 1 kg / l. From this example it follows that the mass of 1 liter of tap water is 1 kg. The same volume of a different substance or substance has a different weight.
It is known that as the temperature decreases, the density of bodies increases.
There are two main methods for determining the density of a substance: areometric and pycnometric. A hydrometer is used to measure the density of various liquids, and a pycnometer is used to measure the density of creams, balms, gels, toothpastes.
Based on the measured density of cosmetic products according to the tables agreed at the enterprise "Limits of permissible deviations of the net content from the nominal quantity" in accordance with GOST 8.579-2002 "Requirements for the number of packaged goods in any type of packaging during their production, packaging, sale and import" limits are determined permissible deviations of the net content of the product from the nominal value.
A hydrometer is a device used to measure the density of various liquids and liquid substances. As a rule, it is a glass tube, the lower part of which is significantly expanded in diameter. During calibration, the expanded part is filled with shot or mercury, which are used to achieve a given mass. At the top of the hydrometer is a graduated scale in certain corresponding density values. Since the density of liquids and liquid substances is very dependent on temperature, therefore, the hydrometer is either equipped with a thermometer, or the temperature of the liquid is simultaneously measured with another thermometer.
To carry out the procedure for measuring the density of a liquid substance or liquid, a clean hydrometer is carefully placed in a measuring beaker with a sufficient volume of liquid, but in such a way that the hydrometer floats freely in it. Density values are determined on the hydrometer scale of the liquid located at the lower edge of the meniscus.
In physics, a hydrometer is a device used to determine the value of density and, consequently, to determine the specific gravity of bodies.
Historians of science believe that Hypatia, a famous female scientist, astronomer, mathematician and philosopher, head of the Alexandrian School of Neoplatonism, invented the hydrometer as a device for taking measurements. Thanks to her scientific activity, other devices were invented or improved: a distiller, an astrolabe and a planisphere.
The device of modern hydrometers, as well as hydrometers used in antiquity, is based on the well-known hydrostatic law - the law of Archimedes. As is known from elementary school, Archimedes' law states that every body floats in a liquid and sinks so deep into it that the weight displaced by this body fluid is equal to the weight of the entire body floating in this fluid.
Interesting circumstances preceded the discovery of the law of Archimedes, which glorified the scientist for all time. “Eureka!” Everyone exclaims, finding a solution to a difficult problem, and yet this is preceded by a whole story.
Archimedes served at the court of Hieron II, the tyrant of Syracuse, who ruled from 270-215 BC, and from 269 BC bore the title of king. Hieron was known as an insidious, greedy and suspicious ruler.
He suspected his jewelers that in the manufacture of gold items they mix silver into gold or worse than that, tin to the noble metal, which was the reason for the discovery of one of the physical laws. He instructed Archimedes to expose the goldsmiths, as he was sure that the goldsmiths had stolen the gold while making the crown for him.
To solve this complex problem, it is necessary to know not only the mass, but also to determine the volume of the manufactured crown, and this was the most difficult in order to further calculate the density of the metal. The crown has a complex and irregular geometric shape; determining its volume is a very difficult task, the solution of which Archimedes pondered for a long time.
The solution was found by Archimedes in an original way when he plunged into the bath - the water level rose sharply after he plunged into the water. The scientist's body displaced an equal volume of water. "Eureka!" - exclaimed Archimedes and ran to the palace, according to legend, without dressing. After that everything was simple. He immersed the crown in water, measured the volume of the displaced fluid and thus determined the volume of the crown.
Thanks to this, Archimedes discovered the principle or, as it is also called, the law of buoyancy. A solid body immersed in a liquid will displace a volume of liquid equal to the volume of the body immersed in the liquid. Any body can float in water if its average density is less than the density of the liquid in which it is placed.
Archimedes' law states that any body that is immersed in a liquid or gas is subject to buoyant forces directed upwards and equal to the weight of the liquid or gas displaced by it.
Until now, mankind has successfully applied the knowledge gained from distant ancestors in many areas of its activity, including the production of cosmetics.
As already mentioned, a pycnometer is also used to measure density. Density measurement using a pycnometer is carried out as follows.
Before testing, it is necessary to wash the pycnometer successively with a solvent to remove traces of the test substance, then with a chromium mixture, water, alcohol, ether, then dry to constant weight and weigh (the weighing result is recorded in grams to the fourth decimal place).
The pycnometer is filled using a funnel or pipette with distilled water slightly above the mark, closed with a cork and placed for 20 minutes in a thermostat with a temperature of (20 ± 0.1) ° C.
When the temperature reaches (20 ± 0.1) ° C, it is necessary to bring the water level in the pycnometer to the mark, quickly removing excess water with a pipette or a strip of filter paper folded into a tube or, adding water to the mark, close the pycnometer with a stopper and place the pycnometer in thermostat with a temperature of (20 ± 0.1) ° C for 10 minutes.
Take the pycnometer out of the thermostat, weigh it, free it from water, dry it, fill the pycnometer with the test liquid and thermostat.
Calculate the density () in g / cm 3 using the formula:
where : m 1 - mass of the pycnometer with the test liquid, g;
m 0 is the mass of an empty pycnometer, g;
m 2 - mass of the pycnometer with water, g;
A - correction for aerostatic forces, calculated by the formula:
A \u003d 0.0012 x V.
where : V is the volume of the pycnometer, cm3;
0.0012 - air density at 200С, g/cm3;
0.9982 - the density of water at 200C, g / cm 3;
The company "KorolevPharm" uses an express method to measure the density of cosmetic products with a thick consistency (emulsions, cream-gels, gels, balms, etc.). Its essence lies in the fact that a calibrated syringe is used for testing.
To determine the density, weigh an empty syringe (the weighing result is recorded in grams to the second decimal place), fill the syringe with distilled water to the maximum mark, then carefully wipe the surface of the syringe and reweigh.
Determine the volume (V) of the syringe using the formula:
where : m 1 - mass of a syringe with water (g), , 0.9982 - density of water at 200C, g/cm3;
Weigh the empty syringe again (the weighing result is recorded in grams to the second decimal place), fill the syringe with cosmetic mass to the maximum mark, avoiding air bubbles.
Wipe the surface of the syringe thoroughly and reweigh it.
Density () in g / cm 3 calculate by the formula:
Where, m 1 - mass of a syringe with a cosmetic product (g), m 0 - mass of an empty syringe (g), V - syringe volume (cm 3)
The test result is taken as the arithmetic mean of the results of two parallel determinations, the discrepancy between which does not exceed 0.01 g/cm 3 .
This method allows you to quickly determine the density of the manufactured cosmetic product.
We put iron and aluminum cylinders of the same volume on the scales. The balance of the scales has been disturbed. Why?
An imbalance means that the masses of the bodies are not the same. The mass of an iron cylinder is greater than that of an aluminum one. But the volumes of the cylinders are equal. This means that a unit volume (1 cm 3 or 1 m 3) of iron has a greater mass than aluminum.
The mass of a substance contained in a unit of volume is called matter density.
To find density, you need to divide the mass of a substance by its volume. Density is denoted by the Greek letter ρ (ro). Then
density = mass / volume,
ρ = m/V .
The SI unit of density is 1 kg/m 3. The densities of various substances are determined experimentally and are presented in the table:
| Substance | ρ, kg / m 3 | ρ, g/cm 3 |
|---|---|---|
| Substance in solid state at 20 °C | ||
| Osmium | 22600 | 22,6 |
| Iridium | 22400 | 22,4 |
| Platinum | 21500 | 21,5 |
| Gold | 19300 | 19,3 |
| Lead | 11300 | 11,3 |
| Silver | 10500 | 10,5 |
| Copper | 8900 | 8,9 |
| Brass | 8500 | 8,5 |
| Steel, iron | 7800 | 7,8 |
| Tin | 7300 | 7,3 |
| Zinc | 7100 | 7,1 |
| Cast iron | 7000 | 7,0 |
| Corundum | 4000 | 4,0 |
| Aluminum | 2700 | 2,7 |
| Marble | 2700 | 2,7 |
| Window glass | 2500 | 2,5 |
| Porcelain | 2300 | 2,3 |
| Concrete | 2300 | 2,3 |
| Salt | 2200 | 2,2 |
| Brick | 1800 | 1,8 |
| plexiglass | 1200 | 1,2 |
| Kapron | 1100 | 1,1 |
| Polyethylene | 920 | 0,92 |
| Paraffin | 900 | 0,90 |
| Ice | 900 | 0,90 |
| Oak (dry) | 700 | 0,70 |
| Pine (dry) | 400 | 0,40 |
| Cork | 240 | 0,24 |
| Liquid at 20 °C | ||
| Mercury | 13600 | 13,60 |
| Sulfuric acid | 1800 | 1,80 |
| Glycerol | 1200 | 1,20 |
| sea water | 1030 | 1,03 |
| Water | 1000 | 1,00 |
| Sunflower oil | 930 | 0,93 |
| Machine oil | 900 | 0,90 |
| Kerosene | 800 | 0,80 |
| Alcohol | 800 | 0,80 |
| Oil | 800 | 0,80 |
| Acetone | 790 | 0,79 |
| Ether | 710 | 0,71 |
| Petrol | 710 | 0,71 |
| Liquid tin (at t= 400 °C) | 6800 | 6,80 |
| Liquid air (at t= -194 °C) | 860 | 0,86 |
| Gas at 0 °C | ||
| Chlorine | 3,210 | 0,00321 |
| Carbon monoxide (IV) (carbon dioxide) | 1,980 | 0,00198 |
| Oxygen | 1,430 | 0,00143 |
| Air | 1,290 | 0,00129 |
| Nitrogen | 1,250 | 0,00125 |
| Carbon monoxide (II) (carbon monoxide) | 1,250 | 0,00125 |
| Natural gas | 0,800 | 0,0008 |
| Water vapor (at t= 100 °C) | 0,590 | 0,00059 |
| Helium | 0,180 | 0,00018 |
| Hydrogen | 0,090 | 0,00009 |
How to understand that the density of water ρ \u003d 1000 kg / m 3? The answer to this question follows from the formula. Mass of water in volume V\u003d 1 m 3 is equal to m= 1000 kg.
From the density formula, the mass of a substance
m = ρ V.
Of two bodies of equal volume, the body with the greater density of matter has the greater mass.
Comparing the density of iron ρ w = 7800 kg/m 3 and aluminum ρ al = 2700 kg/m 3 , we understand why in the experiment 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 the body is measured in cm 3, then to determine the mass of the body it is convenient to use the density value ρ, expressed in g / cm 3.
Let's translate, for example, the density of water from kg / m 3 to g / cm 3:
ρ in \u003d 1000 kg / m 3 \u003d 1000 \ ( \ frac (1000 ~ g) (1000000 ~ cm ^ (3)) \) \u003d 1 g / cm 3.
So, the numerical value of the density of any substance, expressed in g / cm 3, is 1000 times less than its numerical value, expressed in kg / m 3.
Matter density formula ρ = m/V it is used for homogeneous bodies, i.e., 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 value of the measured density. Is there, for example, some cheap metal added inside a gold bar?
As a rule, a substance in a solid state has a greater density than in a liquid state. An exception to this rule are ice and water, consisting of H 2 O molecules. The density of ice is ρ = 900 kg 3 , the density of water is ρ = 1000 kg 3 . The density of ice is less than the density of water, which indicates a less dense packing of molecules (i.e., large distances between them) in the solid state of matter (ice) than in the liquid state (water). In the future, you will meet with 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 made it possible 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 mainly of soil and rocks. The average density of the earth's crust is 2.7 g / cm 3, and the density of 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 , that is, less than the average density of the Earth. It follows from this 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 matter reaches 11.5 g/cm 3 , i.e. approaches the density of lead.
The average density of human body tissues is 1036 kg / m 3, the density of blood (at t\u003d 20 ° C) - 1050 kg / m 3.
A tree has a low density of wood (2 times less than cork) balsa. Rafts, life belts are made from it. A tree grows in Cuba eshinomena spiny-haired, the wood of which has a density 25 times less than the density of water, i.e. ρ ≈ 0.04 g / cm 3. Very high wood density snake tree. Wood sinks in water like a stone.
Finally, the legend of Archimedes.
Already during the lifetime of the famous ancient Greek scientist Archimedes, legends were made about him, the reason for which were 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 a jeweler mixed a significant amount of silver into it. Of course, the crown should have remained intact. It was not difficult for Archimedes to determine the mass of the crown. It was much more difficult 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 had the wrong shape!
Once Archimedes, absorbed in thoughts of the crown, was taking a bath, where he had a brilliant idea. The volume of a 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.
According to the legend, the density of the crown material turned out to be less than the density of pure gold, and the dishonest jeweler was caught cheating.
Let's put iron and aluminum cylinders of the same volume on the scales (Fig. 122). The balance of the scales has been disturbed. Why?
Rice. 122
In lab work, you measured body weight by comparing the weight of kettlebells to body weight. When the weights were in equilibrium, these masses were equal. An imbalance means that the masses of the bodies are not the same. The mass of an iron cylinder is greater than that of an aluminum one. But the volumes of the cylinders are equal. This means that a unit volume (1 cm 3 or 1 m 3) of iron has a greater mass than aluminum.
The mass of a substance contained in a unit of 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/m 3. The densities of various substances have been 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 solid, liquid and gaseous substances
(at normal atmospheric pressure)
How to understand that the density of water ρ \u003d 1000 kg / m 3? The answer to this question follows from the formula. The mass of water in a volume V \u003d 1 m 3 is equal to m \u003d 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 density of iron ρ w = 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 the body is measured in cm 3, then to determine the mass of the body 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, i.e., 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 value of the measured density. Is there, for example, some cheap metal added inside a gold bar?
Think and answer
- How would the balance of the balance change (see Fig. 122) if, instead of an iron cylinder, a wooden cylinder of the same volume was placed on the cup?
- What is density?
- Does the density of a substance depend on its volume? From the mass?
- What units is density measured in?
- How to go 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 a solid state has a greater density than in a liquid state. An exception to this rule are ice and water, consisting of H 2 O molecules. The density of ice is ρ = 900 kg / m 3, the density of water? \u003d 1000 kg / m 3. The density of ice is less than the density of water, which indicates a less dense packing of molecules (i.e., large distances between them) in the solid state of matter (ice) than in the liquid state (water). In the future, you will meet with 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 made it possible 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 mainly of soil and rocks. The average density of the earth's crust is 2.7 g / cm 3, and the density of 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 , that is, less than the average density of the Earth. It follows from this 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 matter reaches 11.5 g/cm 3 , i.e. approaches the density of lead.
The average density of human body tissues is 1036 kg / m 3, the density of blood (at t = 20 ° C) is 1050 kg / m 3.
Balsa wood has a low density of wood (2 times less than cork). Rafts, life belts are made from it. In Cuba, a prickly-haired echinomena 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 density of wood. Wood sinks in water like a stone.
Do it yourself at home
Measure the density of the soap. To do this, use a rectangular bar of soap. Compare the density value you measured with the values obtained by your classmates. Are the obtained density values equal? Why?
Interesting to know
Already during the lifetime of the famous ancient Greek scientist Archimedes (Fig. 124), legends were composed about him, the reason for which were 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 a jeweler mixed a significant amount of silver into it. Of course, the crown should have remained intact. It was not difficult for Archimedes to determine the mass of the crown. It was much more difficult 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 had the wrong shape!
Rice. 124
Once Archimedes, absorbed in thoughts of the crown, was taking a bath, where he had a brilliant idea. The volume of a 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.
According to the legend, the density of the crown material turned out to be less than the density of pure gold, and the dishonest jeweler was caught cheating.
Exercises
- 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 denser and by how much?
- Determine the mass of a concrete slab, the volume of which is V = 3.0 m 3.
- Of what substance is a ball of volume V = 10 cm 3 made, if its mass is m = 71 g?
- Determine the mass of a window pane whose length a = 1.5 m, height b = 80 cm and thickness c = 5.0 mm.
- The 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.
- Steel and aluminum cylinders have the same cross-sectional areas and masses. Which of the cylinders has a greater height and by how much?
Density is the intensity of the distribution of one quantity over another.
The term combines several different concepts, such as: the density of matter; optical density; population density; building density; density of fire and many others. Let us consider two concepts related to non-destructive testing.
1. Density of matter.
In physics, the density of a substance is the mass of this substance contained in a unit volume under normal conditions. Bodies of the same volume, made of different substances, have different masses, which characterizes their density. For example, two cubes of the same size, made of cast iron and aluminum, will differ in weight and density.
To calculate the density of any body, you need to accurately determine its mass and divide it by the exact volume of this body.
kg / m 3
— Units
density in international
system of units (SI)
g/cm 3
— Units
density in the cgs system
We derive a formula for calculating the density.
For example, let's determine the density of concrete. Let's take a concrete cube weighing 2.3 kg with a side of 10 cm. Let's calculate the volume of the cube.
We substitute the data in the formula.
We get a density of 2,300 kg / m 3.
What determines the density of a substance
The density of a substance depends on temperature. So in the vast majority of cases, as the temperature decreases, the density increases. The exception is water, cast iron, bronze and some other substances that behave differently in a certain temperature range. Water, for example, has a maximum density at 4 °C. As the temperature rises or falls, the density will decrease.
The density of a substance also changes when its state of aggregation changes. It grows abruptly as a substance changes from a gaseous state to a liquid state, and then to a solid state. There are also exceptions here: the density of water, bismuth, silicon and some other substances decreases during solidification.
How is the density of a substance measured?
Special devices and devices are used to measure the density of various substances. Thus, the density of liquids and the concentration of solutions is measured by various hydrometers. Several varieties of pycnometers are designed to measure the density of solids, liquids and gases.
2. Optical density.
In physics, optical density is the ability of transparent materials to absorb light, and opaque materials to reflect it. This concept in most cases characterizes the degree of attenuation of light radiation when it passes through layers and films of various substances.
Optical density is usually expressed as a decimal logarithm of the ratio of the radiation flux incident on the object to the flux that has passed through the object or reflected from it:
Optical density \u003d logarithm (radiation flux incident on an object where D is the optical density; F 0 is the radiation flux incident on the object; F is the radiation flux that has passed through the object or reflected from it).
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