Determination of a substance by density. How is the density of a material measured? Density of various materials. Physical research methods

Density- a physical quantity characterizing the physical properties of a substance, which is equal to the ratio of the mass of a body to the volume occupied by this body.

Density (density of a homogeneous body or average density of a heterogeneous body) can be calculated using the formula:

[ρ] = kg/m³; [m] = kg; [V] = m³.

Where m- body mass, V- its volume; the formula is simply a mathematical notation for the definition of the term "density".

All substances consist of molecules, therefore the mass of any body consists of the masses of its molecules. This is similar to how the mass of a bag of candy is the sum of the masses of all the candies in the bag. If all the candies are the same, then the mass of a bag of candies could be determined by multiplying the mass of one candy by the number of candies in the bag.

The molecules of a pure substance are identical. Therefore, the mass of a drop of water is equal to the product of the mass of one water molecule and the number of molecules in the drop.

The density of a substance shows what the mass of 1 m³ of this substance is.

The density of water is 1000 kg/m³, which means that the mass of 1 m³ of water is 1000 kg. This number can be obtained by multiplying the mass of one water molecule by the number of molecules contained in 1 m³ of its volume.
The density of ice is 900 kg/m³, which means that the mass of 1 m³ of ice is 900 kg.
Sometimes the density unit g/cm³ is used, so we can also say that the mass of 1 cm³ of ice is 0.9 g.

Each substance occupies a certain volume. And it may turn out that the volumes of the two bodies are equal, and their masses are different. In this case, they say that the densities of these substances are different.

Also when the masses of two bodies are equal their volumes will be different. For example, the volume of ice is almost 9 times greater than the volume of an iron bar.

The density of a substance depends on its temperature.

As temperature increases, density usually decreases. This is due to thermal expansion, when the volume increases while the mass remains unchanged.

As the temperature decreases, the density increases. Although there are substances whose density behaves differently in a certain temperature range. For example, water, bronze, cast iron. Thus, the density of water has a maximum value at 4 °C and decreases both with increasing and decreasing temperature relative to this value.

When the state of aggregation changes, the density of a substance changes abruptly: the density increases during the transition from a gaseous state to a liquid and when the liquid solidifies. Water, silicon, bismuth and some other substances are exceptions to this rule, since their density decreases when solidified.

Problem solving

Task No. 1.
A rectangular metal plate 5 cm long, 3 cm wide and 5 mm thick has a mass of 85 g. What material can it be made of?

Analysis of a physical problem. To answer the question posed, it is necessary to determine the density of the substance from which the plate is made. Then, using the density table, determine which substance the found density value corresponds to. This problem can be solved in these units (i.e. without conversion to SI).

Task No. 2.
A copper ball with a volume of 200 cm 3 has a mass of 1.6 kg. Determine whether this ball is solid or empty. If the ball is empty, then determine the volume of the cavity.

Analysis of a physical problem. If the volume of copper is less than the volume of the sphere V copper

Task No. 3.
A canister that holds 20 kg of water is filled with gasoline. Determine the mass of gasoline in the canister.

Analysis of a physical problem. To determine the mass of gasoline in a canister, we need to find the density of gasoline and the capacity of the canister, which is equal to the volume of water. The volume of water is determined by its mass and density. We find the density of water and gasoline in the table. It is better to solve the problem in SI units.

Task No. 4.
An alloy was made from 800 cm 3 of tin and 100 cm 3 of lead. What is its density? What is the mass ratio of tin and lead in the alloy?

People come across the word “mass” very often in everyday life. It is written on product packaging, and all the objects around us also have their own unique mass.

Definition 1

Mass is usually understood as a physical quantity that shows the amount of substance contained in a body.

From the physics course we know that all substances consist of constituent elements: atoms and molecules. In different substances, the masses of atoms and molecules are not the same, so the mass of a body depends on the characteristics of ultra-small particles. There is a relationship based on which it is clear that a denser arrangement of atoms in a body increases the total mass and vice versa.

Currently, there are different properties of matter that can be used to characterize mass:

• the body’s ability to resist when its speed changes;
• the ability of the body to be attracted to another object;
• quantitative composition of particles in a certain body;
• the amount of work done by the body.

The numerical value of body weight remains at the same level in all cases. When solving problems, the numerical value of the body mass can be taken the same, since there is no dependence on what property of matter the mass reflects.

Inertia

There are two types of masses:

• inert mass;
• gravitational mass.

The resistance of a body to attempts to change its speed is called inertia. Not all bodies can change their initial speed with the same force, since they have different inertial mass. Some bodies, under the same influence from other bodies that surround it, are able to quickly change their speed, while others, under identical conditions, cannot, that is, they change speed noticeably slower than the first bodies.

Inertia changes based on body mass characteristics. A body that changes speed more slowly has a large mass. A measure of the inertia of a body is the inertial mass of the object. When two bodies interact with each other, the speed of both objects changes. In this case, it is customary to say that the bodies acquire acceleration.

$\frac(a_1)(a_2) = \frac(m_2)(m_1)$

The ratio of the acceleration modules of bodies that interact with each other is equal to the inverse ratio of their masses.

Note 1

Gravitational mass is a measure of the gravitational interaction of bodies. Inertial and gravitational mass are proportional to each other. Equality of gravitational and inertial masses is achieved by choosing a proportionality coefficient. It must be equal to one.

Mass is measured in SI units in kilograms (kg).

Properties of mass

The mass has several fundamental properties:

• it is always positive;
• the mass of a system of bodies is equal to the sum of the masses of the bodies that are included in this system;
• mass in classical mechanics does not depend on the speed of movement of the body and its nature;
• the mass of a closed system is conserved in the case of various interactions of bodies with each other.

To measure the value of mass, a mass standard was adopted at the international level. It is called a kilogram. The standard is stored in France and is a metal cylinder, the height and diameter of which is 39 millimeters. The standard is a value that reflects the ability of a body to be attracted to another body.

Mass in the SI system is denoted by the Latin small letter $m$. Mass is a scalar quantity.

There are several ways to determine mass in practice. The most commonly used method is weighing the body on a scale. This is how gravitational mass is measured. There are different types of scales:

• electronic:
• lever;
• spring.

Measuring body weight by weighing on a scale is the most ancient method. It was used by the inhabitants of Ancient Egypt 4 thousand years ago. Nowadays, scale designs have different shapes and sizes. They make it possible to determine the body weight of ultra-small shapes, as well as multi-ton cargo. Such scales are usually used in transport or industrial enterprises.

The concept of density of matter

Definition 2

Density is a scalar physical quantity that is determined by the mass of a unit volume of a particular substance.

$\rho = \frac(m)(V)$

Density of a substance ($\rho$) is the ratio of the mass of a body $m$ or substance to the volume $V$ that this body or substance occupies.

The SI unit of body density is kg/m $^(3)$.

Note 2

The density of a substance depends on the mass of the atoms that make up the substance, as well as the packing density of the molecules in the substance.

The density of a body increases under the influence of a large number of atoms. Different states of aggregation of a substance significantly change the density of a particular substance.

Solids have a high degree of density because in this state the atoms are very tightly packed. If we consider the same substance in a liquid state of aggregation, then its density will decrease, but will remain at approximately a comparable level. In gases, the molecules of a substance are as far away from each other as possible, so the packing of atoms at this level of aggregation is very low. Substances will have the lowest density.

Currently, researchers are compiling special tables of the densities of various substances. The metals with the highest density are osmium, iridium, platinum, and gold. All these materials are famous for their impeccable strength. Aluminum, glass, concrete have average densities - these materials have special technical characteristics and are often used in construction. Dry pine and cork have the lowest density values, so they do not sink in water. Water has a density of 1000 kilograms per cubic meter.

Scientists were able to use new calculation methods to determine the average density of matter in the Universe. The results of the experiments showed that basically outer space is rarefied, that is, there is practically no density - about six atoms per cubic meter. This means that the mass values ​​at this density will also be unique.

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 the 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).

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.

Figure 1. Table of densities of some substances. Author24 - online exchange of student work

All bodies in the world around us have different sizes and volumes. But even with the same volumetric data, the mass of substances will differ significantly. In physics, this phenomenon is called the density of matter.

Density is a basic physical concept that gives an idea of ​​the characteristics of any known substance.

Definition 1

The density of a substance is a physical quantity that shows the mass of a certain substance per unit volume.

The units of volume in terms of the density of a substance are usually the cubic meter or cubic centimeter. Determination of the density of a substance is carried out using special equipment and instruments.

To determine the density of a substance, it is necessary to divide the mass of its body by its own volume. When calculating the density of a substance, the following values ​​are used:

body weight ($m$); body volume ($V$); body density ($ρ$)

Note 1

$ρ$ is a letter of the Greek alphabet "rho" and should not be confused with a similar designation for pressure - $p$ ("peh").

Substance density formula

The density of a substance is calculated using the SI measurement system. In it, density units are expressed in kilograms per cubic meter or grams per cubic centimeter. You can also use any measurement system.

A substance has different degrees of density if it is in different states of aggregation. In other words, the density of a substance in a solid state will be different than the density of the same substance in a liquid or gaseous state. For example, water has a density in its normal liquid state of 1000 kilograms per cubic meter. In a frozen state, water (ice) will already have a density of 900 kilograms per cubic meter. Water vapor at normal atmospheric pressure and a temperature close to zero degrees will have a density of 590 kilograms per cubic meter.

The standard formula for the density of a substance is as follows:

In addition to the standard formula, which is used only for solids, there is a formula for gas under normal conditions:

$ρ = M / Vm$, where:

• $M$ is the molar mass of the gas,
• $Vm$ is the molar volume of the gas.

There are two types of solids:

• porous;
• bulk.

Note 2

Their physical characteristics directly affect the density of the substance.

Density of homogeneous bodies

Definition 2

The density of homogeneous bodies is the ratio of the mass of a body to its volume.

The concept of density of a substance includes the definition of the density of a homogeneous and uniformly distributed body with a heterogeneous structure, which consists of this substance. This is a constant value and for a better understanding of the information, special tables are formed where all common substances are collected. The values ​​for each substance are divided into three components:

• density of a body in a solid state;
• density of a body in a liquid state;
• density of a body in a gaseous state.

Water is a fairly homogeneous substance. Some substances are not so homogeneous, so the average density of the body is determined for them. To derive this value, it is necessary to know the result ρ of the substance for each component separately. Loose and porous bodies have true density. It is determined without taking into account the voids in its structure. Specific gravity can be calculated by dividing the mass of a substance by the entire volume it occupies.

Similar values ​​are related to each other by the porosity coefficient. It represents the ratio of the volume of voids to the total volume of the body that is currently being examined.

The density of substances depends on many additional factors. A number of them simultaneously increase this value for some substances, and decrease them for others. At low temperatures, the density of the substance increases. Some substances are able to react to changes in temperature in different ways. In this case, it is customary to say that the density behaves anomalously at a certain temperature range. Such substances often include bronze, water, cast iron and some other alloys. The density of water is greatest at 4 degrees Celsius. With further heating or cooling, this indicator can also change significantly.

Metamorphoses with the density of water occur during the transition from one state of aggregation to another. The indicator ρ changes its values ​​in these cases in an abrupt manner. It progressively increases during the transition to a liquid from a gaseous state, as well as at the moment of crystallization of the liquid.

There are many exceptional cases. For example, silicon has low density values ​​when solidified.

Measuring the density of matter

To effectively measure the density of a substance, special equipment is usually used. It consists of:

• scales;
• measuring instrument in the form of a ruler;
• volumetric flask.

If the substance under study is in a solid state, then a measure in the form of a centimeter is used as a measuring device. If the substance under study is in a liquid aggregate state, then a volumetric flask is used for measurements.

First, you need to measure your body volume using a centimeter or measuring flask. The researcher observes the measurement scale and records the resulting result. If a cube-shaped wooden beam is examined, then the density will be equal to the value of the side raised to the third power. When studying a liquid, it is necessary to additionally take into account the mass of the vessel with which the measurements are taken. The obtained values ​​must be substituted into the universal formula for the density of the substance and the indicator calculated.

For gases, calculating the indicator is very difficult, since it is necessary to use various measuring instruments.

Typically, a hydrometer is used to calculate the density of substances. It is designed to obtain results from liquids. True density is studied using a pycnometer. The soils are examined using Kaczynski and Seidelman drills.