Density is usually called a physical quantity that determines the ratio of the mass of an object, substance or liquid to the volume they occupy in space. Let's talk about what density is, how the density of a body and matter differs, and how (with which formula) to find density in physics.
Density types
It should be clarified that the density can be subdivided into several types.
Depending on the object under study:
- The density of a body - for homogeneous bodies - is the direct ratio of body mass to its volume occupied in space.
- The density of a substance is the density of bodies consisting of this substance. The density of substances is constant. There are special tables where the density of different substances is indicated. For example, the density of aluminum is 2.7 * 103 kg / m 3. Knowing the density of aluminum and the mass of the body that is made of it, we can calculate the volume of this body. Or, knowing that the body consists of aluminum and knowing the volume of this body, we can easily calculate its mass. We will consider how to find these values \u200b\u200ba little later, when we derive the formula for calculating the density.
- If a body consists of several substances, then to determine its density, it is necessary to calculate the density of its parts for each substance separately. This density is called the average body density.
Depending on the porosity of the substance of which the body is composed:
- True density is that density that is calculated without taking into account the voids in the body.
- Specific gravity - or apparent density - is one that is calculated taking into account the voids of a body consisting of a porous or friable substance.
So how do you find density?
Formula for calculating density
The formula to help find the density of a body is as follows:
- p \u003d m / V, where p is the density of the substance, m is the mass of the body, V is the volume of the body in space.
If we calculate the density of this or that gas, then the formula will look like this:
- p \u003d M / V m p is the density of the gas, M is the molar mass of the gas, V m is the molar volume, which under normal conditions is 22.4 l / mol.
Example: the mass of a substance is 15 kg, it takes up 5 liters. What is the density of the substance?
Solution: substitute values \u200b\u200bin the formula
- p \u003d 15/5 \u003d 3 (kg / l)
Answer: the density of the substance is 3 kg / l
Density units
In addition to knowing how to find the density of a body and matter, you need to know the units of density measurement.
- For solids - kg / m 3, g / cm 3
- For liquids - 1 g / l or 10 3 kg / m 3
- For gases - 1 g / l or 10 3 kg / m 3
You can read more about density units in our article.
How to find density at home
In order to find the density of a body or substance at home, you will need:
- Libra;
- A centimeter if the body is solid;
- A vessel if you want to measure the density of a liquid.
To find the density of a body at home, you need to measure its volume with a centimeter or vessel, and then put the body on a scale. If you are measuring the density of a liquid, do not forget to subtract the mass of the vessel into which you poured the liquid before calculating. The density of gases at home is much more difficult to calculate, we recommend using ready-made tables, in which the densities of various gases are already indicated.
The bodies around us are composed 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 is composed. Bodies of the same volume, consisting of different substances, have different masses. For example, having weighed two cylinders of different substances - aluminum and lead, we will see that the mass of aluminum 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. So, an iron bar weighing 1 ton occupies a volume of 0.13 m 3, and ice weighing 1 ton - 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.
Hence it follows that bodies with the same volume, consisting of different substances, have different masses.
Density shows what is the mass of a substance taken in a certain volume. That is, if you know the mass of the body and its volume, you can determine the density. To find the density of a substance, the mass of the body must be divided by its volume.
The density of one and the same substance in solid, liquid and gaseous states is different.
The density of some solids, liquids and gases is given in tables.
Density of some solids (at normal atm. Pressure, t \u003d 20 ° C).
|
Solid |
ρ , kg / m 3 |
ρ , g / cm 3 |
Solid |
ρ , kg / m 3 |
ρ , g / cm 3 |
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Window glass |
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Pine (dry) |
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Plexiglass |
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Rafinated sugar |
Polyethylene |
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Oak (dry) |
Density of some liquids (at normal atm. Pressure t \u003d 20 ° C).
|
Liquid |
ρ , kg / m 3 |
ρ , g / cm 3 |
Liquid |
ρ , kg / m 3 |
ρ , g / cm 3 |
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The water is clean |
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Whole milk |
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Sunflower oil |
Liquid tin (at t \u003d 400 °C) |
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Machine oil |
Liquid air (at t \u003d -194 °C) |
A table of the density of liquids at various temperatures and atmospheric pressure is given for the most common liquids. Density values \u200b\u200bin 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 able to change 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 consider examples of density of some liquids. The first substance that comes to mind when the word "liquid" is water. And this is not at all accidental, because water is the most widespread substance on the planet, and therefore it can be taken as an ideal.
Equal to 1000 kg / m 3 for distilled water and 1030 kg / m 3 for seawater. Since this value is closely related to temperature, it should be noted 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 close in value to different food products. These are products such as: vinegar solution, wine, 20% cream and 30% sour cream. Individual products are denser, for example, egg yolk - its density is 1042 kg / m 3. For example, it turns out to be denser than water: pineapple juice - 1084 kg / m 3, grape juice - up to 1361 kg / m 3, orange juice - 1043 kg / m 3, coca-cola and beer - 1030 kg / m 3.
Many substances are inferior in density to water. For example, alcohols are much lighter than water. So the density is 789 kg / m 3, butyl - 810 kg / m 3, methyl - 793 kg / m 3 (at 20 ° C). Certain types of fuel and oil have even lower density values: oil - 730-940 kg / m 3, gasoline - 680-800 kg / m 3. The density of kerosene is about 800 kg / m 3 - 879 kg / m 3, fuel oil - up to 990 kg / m 3.
| Liquid | Temperature, ° C |
Density of liquid, kg / m 3 |
|---|---|---|
| Aniline | 0…20…40…60…80…100…140…180 | 1037…1023…1007…990…972…952…914…878 |
| (GOST 159-52) | -60…-40…0…20…40…80…120 | 1143…1129…1102…1089…1076…1048…1011 |
| Acetone C 3 H 6 O | 0…20 | 813…791 |
| Chicken egg white | 20 | 1042 |
| 20 | 680-800 | |
| 7…20…40…60 | 910…879…858…836 | |
| Bromine | 20 | 3120 |
| Water | 0…4…20…60…100…150…200…250…370 | 999,9…1000…998,2…983,2…958,4…917…863…799…450,5 |
| Sea water | 20 | 1010-1050 |
| The water is heavy | 10…20…50…100…150…200…250 | 1106…1105…1096…1063…1017…957…881 |
| Vodka | 0…20…40…60…80 | 949…935…920…903…888 |
| Fortified wine | 20 | 1025 |
| Dry wine | 20 | 993 |
| Gas oil | 20…60…100…160…200…260…300 | 848…826…801…761…733…688…656 |
| 20…60…100…160…200…240 | 1260…1239…1207…1143…1090…1025 | |
| GTP (coolant) | 27…127…227…327 | 980…880…800…750 |
| Dowtherm | 20…50…100…150…200 | 1060…1036…995…953…912 |
| Chicken egg yolk | 20 | 1029 |
| Carboran | 27 | 1000 |
| 20 | 802-840 | |
| Nitric acid HNO 3 (100%) | -10…0…10…20…30…40…50 | 1567…1549…1531…1513…1495…1477…1459 |
| Palmitic acid C 16 H 32 O 2 (conc.) | 62 | 853 |
| Sulfuric acid H 2 SO 4 (conc.) | 20 | 1830 |
| Hydrochloric acid HCl (20%) | 20 | 1100 |
| Acetic acid CH 3 COOH (conc.) | 20 | 1049 |
| Cognac | 20 | 952 |
| Creosote | 15 | 1040-1100 |
| 37 | 1050-1062 | |
| Xylene C 8 H 10 | 20 | 880 |
| Copper sulfate (10%) | 20 | 1107 |
| Copper sulfate (20%) | 20 | 1230 |
| Cherry liqueur | 20 | 1105 |
| Fuel oil | 20 | 890-990 |
| Peanut butter | 15 | 911-926 |
| Machine oil | 20 | 890-920 |
| Motor oil T | 20 | 917 |
| Olive oil | 15 | 914-919 |
| (refined.) | -20…20…60…100…150 | 947…926…898…871…836 |
| Honey (dehydrated) | 20 | 1621 |
| Methyl acetate CH 3 COOCH 3 | 25 | 927 |
| 20 | 1030 | |
| Condensed milk with sugar | 20 | 1290-1310 |
| Naphthalene | 230…250…270…300…320 | 865…850…835…812…794 |
| Oil | 20 | 730-940 |
| Drying oil | 20 | 930-950 |
| Tomato paste | 20 | 1110 |
| Boiled molasses | 20 | 1460 |
| Starch syrup | 20 | 1433 |
| A PUB | 20…80…120…200…260…340…400 | 990…961…939…883…837…769…710 |
| Beer | 20 | 1008-1030 |
| PMS-100 | 20…60…80…100…120…160…180…200 | 967…934…917…901…884…850…834…817 |
| PES-5 | 20…60…80…100…120…160…180…200 | 998…971…957…943…929…902…888…874 |
| Apple puree | 0 | 1056 |
| (10%) | 20 | 1071 |
| A solution of sodium chloride in water (20%) | 20 | 1148 |
| Sugar in water solution (saturated) | 0…20…40…60…80…100 | 1314…1333…1353…1378…1405…1436 |
| Mercury | 0…20…100…200…300…400 | 13596…13546…13350…13310…12880…12700 |
| Carbon disulfide | 0 | 1293 |
| Silicone (diethylpolysiloxane) | 0…20…60…100…160…200…260…300 | 971…956…928…900…856…825…779…744 |
| Apple syrup | 20 | 1613 |
| Turpentine | 20 | 870 |
| (fat content 30-83%) | 20 | 939-1000 |
| Resin | 80 | 1200 |
| Coal tar | 20 | 1050-1250 |
| Orange juice | 15 | 1043 |
| Grape juice | 20 | 1056-1361 |
| Grapefruit juice | 15 | 1062 |
| Tomato juice | 20 | 1030-1141 |
| Apple juice | 20 | 1030-1312 |
| Amyl alcohol | 20 | 814 |
| Butyl alcohol | 20 | 810 |
| Isobutyl alcohol | 20 | 801 |
| Isopropyl alcohol | 20 | 785 |
| Methyl alcohol | 20 | 793 |
| Propyl alcohol | 20 | 804 |
| Ethyl alcohol C 2 H 5 OH | 0…20…40…80…100…150…200 | 806…789…772…735…716…649…557 |
| Sodium-potassium alloy (25% Na) | 20…100…200…300…500…700 | 872…852…828…803…753…704 |
| Lead-bismuth alloy (45% Pb) | 130…200…300…400…500..600…700 | 10570…10490…10360…10240…10120..10000…9880 |
| liquid | 20 | 1350-1530 |
| Milk whey | 20 | 1027 |
| Tetracresiloxysilane (CH 3 C 6 H 4 O) 4 Si | 10…20…60…100…160…200…260…300…350 | 1135…1128…1097…1064…1019…987…936…902…858 |
| Tetrachlorodiphenyl C 12 H 6 Cl 4 (arochlor) | 30…60…150…250…300 | 1440…1410…1320…1220…1170 |
| 0…20…50…80…100…140 | 886…867…839…810…790…744 | |
| Diesel fuel | 20…40…60…80…100 | 879…865…852…838…825 |
| Carburetor fuel | 20 | 768 |
| Motor fuel | 20 | 911 |
| Fuel RT | 836…821…792…778…764…749…720…692…677…648 | |
| Fuel T-1 | -60…-40…0…20…40…60…100…140…160…200 | 867…853…824…819…808…795…766…736…720…685 |
| Fuel T-2 | -60…-40…0…20…40…60…100…140…160…200 | 824…810…781…766…752…745…709…680…665…637 |
| Fuel T-6 | -60…-40…0…20…40…60…100…140…160…200 | 898…883…855…841…827…813…784…756…742…713 |
| Fuel T-8 | -60…-40…0…20…40…60…100…140…160…200 | 847…833…804…789…775…761…732…703…689…660 |
| Fuel TS-1 | -60…-40…0…20…40…60…100…140…160…200 | 837…823…794…780…765…751…722…693…879…650 |
| Carbon tetrachloride (CTC) | 20 | 1595 |
| Urotoropin C 6 H 12 N 2 | 27 | 1330 |
| Fluorobenzene | 20 | 1024 |
| Chlorobenzene | 20 | 1066 |
| Ethyl acetate | 20 | 901 |
| Ethyl bromide | 20 | 1430 |
| Ethyl iodide | 20 | 1933 |
| Ethyl chloride | 0 | 921 |
| Ether | 0…20 | 736…720 |
| Aether of Garpius | 27 | 1100 |
Low density indicators are distinguished by such liquids as: turpentine 870 kg / m 3,
§ 9. What is the density of matter?
What do they mean when they say: heavy as lead or light as down? It is clear that a grain of lead will be light, and at the same time, a mountain of fluff will have a fair mass. Those who use such comparisons do not mean the mass of bodies, but some other characteristic.
Often in life you can find bodies with the same volume, but different masses. For example, a tomato and a small ball. And in the store there is a large selection of products that have equal weights, but differ in volume, for example, a pack of butter and a bag of corn sticks. It follows from this that bodies of equal mass can have different volumes, and bodies of the same volume can differ in mass. This means that there is a certain physical quantity that connects both of these characteristics. This value was called density (denoted by the letter of the Greek alphabet ρ - ro).
Density is a physical quantity that is numerically equal to the mass of 1 cm3 of a substance. Density unit kg / m3 or g / cm3. Thus, the density of a substance does not change under constant conditions and does not depend on the volume of the body.
There are several ways to determine the density of a substance. One of these methods is to determine the mass of a substance by weighing and measuring the volume it occupies. Using these values, you can calculate the density by dividing body weight by its volume.
Body mass t
Density \u003d ----- or ρ = --
Body volume V
It is not always necessary to calculate the density of a substance. So, to measure the density of a liquid there is a device - hydrometer. It is immersed in a liquid, depending on the density of the liquid, the hydrometer is immersed in it at different depths.
Knowing the density of the substance and the volume of the body, you can calculate the weight of the body and do without weights, t \u003d V * ρ
Knowing the density of the substance and the mass of the body, it is easy to calculate its volume.
V \u003dm /ρ
This is very convenient when the shape of the body under study is complex, for example, a snail shell or a mineral fragment.
A bit of history. It was in this way that the famous Archimedes of the Syracuse jeweler, who made a crown not of pure gold for King Heron 250 years before our era, caught in a lie. The density of the corona material was found to be less than that of gold. The jeweler, however, did not anticipate exposure, for the shape of the crown was incredibly complex.
The densities of various substances are determined and entered in special tables. You have such a table in your exercise book on page 22.
From the table given in the exercise book it can be seen that the substances in the gaseous state have the lowest density; the largest - substances in a solid state. This is due to the fact that molecules in gases are located far from each other, and molecules in solids are close. Therefore, the density of a substance is related to how close or far the molecules are. And the molecules of different substances themselves differ both in mass and in size.
Different substances have different densities, which depend on the mass and size of the molecules, as well as on their relative position. The density of a substance can be calculated by knowing its mass and body volume. There is a hydrometer device for measuring the density of liquids, and special tables have been compiled to determine the density of various substances.
Hydrometer * Density of substances
Test your knowledge
1. What physical quantity is called the density of a substance?
2. What quantities do you need to know to calculate the density of a substance?
3. What instrument can be used to determine the density of a liquid? How does it work?
4. Using the table of the density of substances, determine the density: aluminum, distilled water, honey.
5. Using the table of substance density, name:
a) the substance with the highest density;
b) with the lowest density;
c) with a density greater than that of distilled water.
b. In nature, substances with different densities often interact. Using the density table, explain why:
a) ice is always located on the surface of the water;
b) a gasoline film floats on the surface of a puddle;
c) is it easier for a person to swim in sea water than in fresh water?
The study of the density of substances begins in the high school physics course. This concept is considered fundamental in the further presentation of the foundations of the molecular kinetic theory in physics and chemistry courses. The purpose of studying the structure of matter, research methods, one can assume the formation of scientific ideas about the world.
Physics gives the initial idea of \u200b\u200ba unified picture of the world. The 7th class studies the density of a substance on the basis of the simplest ideas about research methods, the practical application of physical concepts and formulas.
Physical research methods
As you know, observation and experiment are distinguished among the methods of studying natural phenomena. They teach in elementary school to observe natural phenomena: they carry out the simplest measurements, often keep a "Nature Calendar". These forms of education are capable of leading a child to the need to study the world, compare the observed phenomena, and identify cause-and-effect relationships.
However, only a fully-fledged 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.
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. Turning to the child's experience, considering the facts known to him 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 problematic teaching method at the beginning of the lesson, you can ask the well-known riddle: "Which is heavier: a kilogram of fluff or a kilogram of cast iron?" Of course, 11-12-year-olds easily give an answer to a 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 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 matter. The indication of the difference in the physical properties of solids, liquids and gases, considered 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 matter, takes the study of physics to a different level.
To consolidate knowledge about the physical meaning of the concept under study, the table of density of substances allows. A 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 the static nature of 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 relation of quantities for children. She is given special attention not only due to the study of the concepts of density, but also due to the fact of learning methods of solving problems.
It is at this stage that the algorithm for solving a physical computational problem, the ideology of applying the basic formulas, definitions, and patterns is laid. The teacher tries to teach the analysis of the problem, the method of searching for the unknown, the peculiarities of using the units of measurement by using such a ratio as the density formula in physics.
Example of problem solving
Example 1
Determine from which substance the cube weighing 540 g and a volume of 0.2 dm 3 is made.
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 densities of solids will help us to 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, therefore the volume is converted from dm 3 to cm 3.
Decision
By definition: ρ \u003d 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.
Determination of other quantities
Using the formula for calculating the density allows you to determine other physical quantities. Mass, volume, linear dimensions of bodies associated with volume can be easily calculated in problems. Knowledge of mathematical formulas for determining the area and volume of geometric shapes is used in problems, which makes it possible to clarify the need to study mathematics.
Example 2
Determine the thickness of the copper layer, which covers a part with a surface area of \u200b\u200b500 cm 2, if it is known that 5 g of copper was consumed 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 value of the density of copper.
Let's use the formula for calculating the density. This formula contains the volume of the substance, from which the linear dimensions can be determined.
Decision
By definition: ρ \u003d m: V, but this formula does not contain the desired value, so we use:
Substituting into the main formula, we get: ρ \u003d m: Sh, whence:
We 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 microns.
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 the 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 the liquid using the formula.
- Determination of the density of a substance of a solid with a regular shape. This task is also not in doubt, since similar computational problems have already been considered and experience has been gained in measuring volumes by linear dimensions of bodies.
- Determination of the density of a solid of irregular shape. When performing this task, we use the method of determining the volume of an irregularly shaped body using a beaker. It is not out of place to once again recall the features of this method: the ability of a solid to displace a liquid whose volume is equal to the volume of the body. Further, the problem is solved in the standard way.
Advanced tasks
You can complicate the task by asking the children to determine the substance from which the body is made. The table of density 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 must have the necessary amount of knowledge in the use and translation of units of measurement. This is often what causes the greatest number of errors and shortcomings. Perhaps, this stage of studying physics should be allocated more time, it allows you to compare knowledge and research experience.
Bulk density
The study of pure substances is, of course, interesting, but how often are pure substances found? In everyday life, we meet with 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 \u200b\u200bof the density of substances.
It is extremely necessary to clarify this issue, to make it possible to see and feel the difference between the density of a substance and bulk density is in the early stages. Understanding this difference is necessary in the further study of physics.
This difference is extremely interesting in the case of Allowing 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 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 the school course in natural history, it is interesting for deep study (most often optional).
The Olympiad level of studying physics and chemistry can also affect the concept of "relative density of matter in terms of hydrogen". It is usually applied to gases. To determine the relative density of the gas, the ratio of the molar mass of the test gas to the use is not excluded.