physical density. Density determination

Instruction

Knowing the above two values, you can write a formula for calculating the density substances: density = mass / volume, hence the desired value is obtained. Example. It is known that an ice floe with a volume of 2 cubic meters is 1800 kg. Find the density of ice. Solution: the density is 1800 kg / 2 meters cubed, it turns out 900 kg divided by cubic. Sometimes you have to convert density units to each other. In order not to get confused, you should remember: 1g / cm cubed is equal to 1000 kg / m3 cubed. Example: 5.6 g / cm cubed is 5.6 * 1000 \u003d 5600 kg / m cubed.

Water, like any liquid, cannot always be weighed on a scale. But find out mass it is necessary both in some industries and in ordinary everyday situations, from calculating reservoirs to deciding how much stock water you can take with you in a kayak or rubber boat. In order to calculate mass water or any liquid placed in this or that volume, first of all it is necessary to know its density.

You will need

measuring utensils
Ruler, tape measure or any other measuring device
Vessel for pouring water

Instruction

If you need to calculate mass water in a small vessel, this can be done using conventional scales. Weigh the vessel first with . Then pour the water into another bowl. Then weigh the empty vessel. Subtract from the full vessel mass empty. This is what will be contained in the vessel water. Thus it is possible mass not only liquid, but also loose, if it is possible to pour them into other dishes. This method can sometimes still be observed in some stores where there is no equipment. The seller first weighs an empty jar or bottle, then fills it with sour cream, weighs it again, determines the weight of the sour cream, and only then calculates its cost.

In order to determine mass water in a vessel that cannot be weighed, two parameters must be known - water(or any other liquid) and the volume of the vessel. Density water is 1 g/ml. The density of another liquid can be found in a special table, which is usually found in reference books.

If there is no measuring vessel into which water can be poured, calculate the volume of the vessel in which it is located. The volume is always equal to the product of the area of the base and the height, and there are usually no problems with vessels of a standing shape. Volume water in a jar will be equal to the area of the round base to the height filled with water. Multiplying the density? per volume water V you will receive mass water m: m=?*V.

Matter density: definition and formula

The definition of the density of a substance is as follows: density shows what the mass of a substance is equal to in a unit volume, for example, in one cubic meter. So, the density of water is 1000 kg / m3, and ice - 900 kg / m3, which is why ice is lighter and is located on top in winter on reservoirs. That is, what does the density of matter show us in this case? The density of ice equal to 900 kg/m3 means that a cube of ice with sides of 1 meter weighs 900 kg. And the formula for determining the density of a substance is as follows: density \u003d mass / volume. The quantities included in this expression are denoted as follows: mass - m, volume of the body -V, and density is denoted by the letter ρ (Greek letter "ro"). 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 the volume of the body and body weight. That is, we measure the substance, weigh it, and then we 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 such a value as a gram 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 \u003d 1000 kg / m ^ 3. It should also be remembered that the density of a substance is different in different states of aggregation. That is, solid, liquid, or gaseous. The density of solids, most often, is 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 you know, originated from the oceans. And if water behaved like all other substances, then the water in the seas and oceans would freeze through, ice, being heavier than water, would sink to the bottom and lie there without melting. And only at the equator in a small water column would life exist in the form of several types of bacteria. So we can say thank you to water for the fact that we exist.

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

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 a cubic meter or a cubic centimeter. Determination of the density of a substance is carried out with special equipment and instruments.

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

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

Remark 1

$ρ$ is the letter of the Greek alphabet "ro" and should not be confused with the similar symbol for pressure - $p$ ("pe").

Matter Density Formula

The calculation of the density of a substance occurs with the use of 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 system of measurement.

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 from the density of the same substance in a liquid or gaseous state. For example, water has a density in its normal liquid state of 1,000 kilograms per cubic meter. In the 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:

$M$ - molar mass of gas,
$Vm$ - molar volume of gas.

There are two types of solids:

porous;
loose.

Remark 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 definition of the density of a homogeneous and uniformly distributed body with an inhomogeneous structure, which consists of this substance, is included in the concept of the density of a 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:

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

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

Similar values are interconnected 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 lower it for the rest. At low temperatures, the density of a substance increases. Some substances are able to respond to temperature changes in different ways. In this case, it is customary to say that the density at a certain temperature range behaves anomalously. Such substances often include bronze, water, cast iron and some other alloys. The density of water is highest 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 index ρ in these cases changes its values abruptly. It progressively increases upon transition to a liquid from a gaseous state, as well as at the moment of liquid crystallization.

There are, and many, exceptional cases. For example, silicon has small density values during solidification.

Measuring the density of a substance

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

scales;
measuring device in the form of a ruler;
measuring flask.

If the test substance is in a solid state, then a measuring device in the form of a centimeter is used as a measuring device. If the test substance is in a liquid state of aggregation, then a volumetric flask is used for measurements.

First you have to measure the volume of the body with a centimeter or volumetric flask. The researcher observes the measurement scale and records the result. If a wooden beam of a cubic shape is being examined, then the density will be equal to the value of the side raised to the third power. When examining a liquid, it is necessary to additionally take into account the mass of the vessel with which measurements are taken. The obtained values \u200b\u200bmust be substituted into the universal formula for the density of the substance and the indicator calculated.

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

Usually, a hydrometer is used to calculate the density of substances. It is designed to get results on liquids. The true density is studied using a pycnometer. Soils are examined with the help of Kaczynski and Seidelman drills.

In many industries, as well as in construction and agriculture, the concept of "material density" is used. This is a calculated value, which is the ratio of the mass of a substance to the volume it occupies. Knowing such a parameter, for example, for concrete, builders can calculate the required amount of it when pouring various reinforced concrete structures: building blocks, ceilings, monolithic walls, columns, protective sarcophagi, pools, gateways and other objects.

How to determine the density

It is important to note that, when determining the density of building materials, you can use special reference tables, where these values are given for various substances. Calculation methods and algorithms have also been developed that make it possible to obtain such data in practice if there is no access to reference materials.

Density is determined from:

liquid bodies with a hydrometer device (for example, the well-known process of measuring the parameters of the electrolyte of a car battery);
solid and liquid substances using a formula with known initial data of mass and volume.

All independent calculations, of course, will have inaccuracies, because it is difficult to reliably determine the volume if the body has an irregular shape.

Uncertainties in Density Measurements

The error is systematic. It appears constantly or can change according to a certain law in the process of several measurements of the same parameter. It is associated with the error of the instrument scale, low sensitivity of the device, or the degree of accuracy of the calculation formulas. So, for example, by determining body weight using weights and ignoring the effect of buoyancy, the data is approximate.
The error is random. It is caused by incoming reasons and has a different effect on the reliability of the data being determined. Changes in ambient temperature, atmospheric pressure, vibrations in the room, invisible radiation and air vibrations - all this is reflected in the measurements. It is completely impossible to avoid such influence.

Error in rounding values. When obtaining intermediate data in the calculation of formulas, numbers often have many significant digits after the decimal point. The need to limit the number of these characters implies the appearance of an error. This inaccuracy can be partially reduced by leaving in the intermediate calculations several orders of magnitude more than the final result requires.
Negligence errors (misses) arise due to erroneous calculations, incorrect inclusion of measurement limits or the device as a whole, illegibility of control records. The data obtained in this way can differ sharply from similar calculations. Therefore, they should be deleted and the work done again.

True Density Measurement

Considering the density of the building material, you need to take into account its true indicator. That is, when the structure of the substance of a unit volume does not contain shells, voids and foreign inclusions. In practice, there is no absolute uniformity when, for example, concrete is poured into a mold. To determine its real strength, which directly depends on the density of the material, the following operations are carried out:

The structure is subjected to grinding to a state of powder. At this stage, get rid of the pores.
Dry at a temperature of over 100 degrees, the remaining moisture is removed from the sample.
Cool to room temperature and pass through a fine sieve with a mesh size of 0.20 x 0.20 mm, giving uniformity to the powder.
The resulting sample is weighed on a high precision electronic balance. The volume is calculated in a volumetric meter by immersion in a liquid structure and measurement of the displaced liquid (pycnometric analysis).

The calculation is carried out according to the formula:

where m is the mass of the sample in g;

V is the value of the volume in cm 3.

Density measurement in kg/m 3 is often applicable.

Average material density

To determine how building materials behave in real operating conditions under the influence of moisture, positive and negative temperatures, mechanical loads, you need to use the average density. It characterizes the physical state of materials.

If the true density is a constant value and depends only on the chemical composition and structure of the crystal lattice of the substance, then the average density is determined by the porosity of the structure. It is the ratio of the mass of material in a homogeneous state to the volume of space occupied in natural conditions.

The average density gives the engineer an idea of the mechanical strength, degree of moisture absorption, thermal conductivity and other important factors used in the construction of elements.

The concept of bulk density

Introduced for the analysis of bulk building materials (sand, gravel, expanded clay, etc.). The indicator is important for calculating the cost-effective use of certain components of the building mixture. It shows the ratio of the mass of a substance to the volume that it occupies in a state of loose structure.

For example, if the granular material and the average grain density are known, then it is easy to determine the voidage parameter. In the manufacture of concrete, it is more expedient to use a filler (gravel, crushed stone, sand), which has a lower porosity of the dry matter, since the base cement material will be used to fill it, which will increase the cost.

Density values of some materials

If we take the calculated data of some tables, then in them:

materials, which contain oxides of calcium, silicon and aluminum, varies from 2400 to 3100 kg per m 3.
Tree species with a base of cellulose - 1550 kg per m 3.
Organics (carbon, oxygen, hydrogen) - 800-1400 kg per m 3.
Metals: steel - 7850, aluminum - 2700, lead - 11300 kg per m 3.

With modern building construction technologies, the material density indicator is important from the point of view of the strength of load-bearing structures. All heat-insulating and moisture-proof functions are performed by low-density materials with a closed-pore structure.

All construction and operational properties of building materials can be divided into several groups. Let's list them:

physical properties;
thermophysical;
hydrophysical;
chemical;
mechanical.

Let's talk first about what the basic physical properties of materials are.

One of the most important physical properties is, of course, the density, which can be true and average.

True density is defined as the ratio of the mass of an absolutely dense material (i.e., a material in which there are no voids normally present in its normal, natural state) to its volume. Material Density Calculation(we are talking, of course, about the true density) occurs according to the following formula:

Where m is the mass of the material (measured in grams), Va is its volume in an absolutely dense state (measured in cm3), and ρ is the true density (measured in g/cm3).

The value of the true density shows how much the substance that underlies the material is heavy or light. It is worth noting that the calculation of the density of the material in this option is only auxiliary, to determine it, they use a special device- a volume meter (its other name is the Le Chatelier device). It represents, in fact, a measuring cylinder into which water or any other liquid that does not enter into a chemical reaction with the analyzed material is poured. It works like this: in the process of research, the material is very much crushed, then weighed and then poured into the device, while receiving data on its volume due to the displaced liquid. And then, according to the above formula, the density of the material is directly calculated.

The true density of building materials can vary significantly: for example, for steel it is 7.85 g / cm3, for granite - 2.9 g / cm3, for wood - 1.6 g / cm3 (this value is average and depends on the material used) .

The second type of density (average density of building materials) is the mass per unit volume of the material in its natural form (i.e., together with voids - pores and cracks).

How is the average density determined? The formula for determining it is:

where ρm is the average density, m is the mass of the material, Ve is the volume of the material in its natural form.

The volume of material is determined in various ways - it depends on what shape the sample or product has. The very value of the average density varies, again, in a fairly significant range: from 10-20 kg / m3 (polystyrene foam) to 2500 g / cm3 (heavy concrete). In principle, there are materials with a higher average density.

The average density of building materials depends on the following factors:

on the porosity of the material: if the porosity is zero, then the average density will be equal to the true density, and if the porosity increases, the average density decreases (inverse relationship);
on the moisture content of the material: the higher the average density, the more water in the building material (based on this, the calculation of the density of the material occurs when it is completely dry).

Many physical properties of building materials (for example, strength, thermal conductivity, water absorption) can be found precisely based on the value of their average density.

Describing basic physical properties of materials, one cannot but mention the porosity, which shows how much the volume of the material is filled with voids in the form of pores and cracks. Calculate porosity of building materials can be done using the following formula:

where P is the porosity (%), Vpor is the pore volume in the material under study, Ve is the volume of the material sample in its natural form.

Also, the porosity of building materials is calculated using other formulas.

The porosity of materials used in construction varies over a fairly wide range. So, for example, for glass, polymers and metal, it is 0%, for granite - 0.2-0.8%, and for heat-insulating plasters, porosity can reach 75%.

Distinguish between open and closed porosity of building materials. They differ from each other in that in the first case the pores are open and communicate with the environment, and in the second they are closed. As a rule, in the same material there are two types of pores at once - both closed and open. Porosity has a significant effect on some performance properties of building materials: for example, in sound-absorbing materials, to improve sound absorption, open pores are specially made and the surface is perforated.

The main physical properties of materials are not limited to density and porosity - There is also such a thing as "emptiness", which is used when talking about products specially created with voids inside (there are such voids in ceramic bricks). As for the definition, the value of voidness characterizes the degree of filling the volume of the product under consideration with voids.