How to find volume in physics - moskovdom.ru

Meaning of the word; volume

The meaning of the word "volume"

Volume , -but, m.

one. Magnitude of In length, height and width, measured in cubic units. The volume of the geometric body. Cube volume. The volume of the building.

2. Content of From the point of view of the magnitude, size, quantity, etc. Scope of work. Retail volume. Volume of knowledge. Amount of information. The literary inheritance Garshin is very small in volume. Korolenko, V. M. Garin.

Source (print version): Dictionary of the Russian language: in 4 tons / wounds, Institute Linguistich. studies; Ed. A. P. Evgenaya. - 4th ed., Ched. - M.: Rus. Yaz.; Poligraphressurs, 1999; (electronic version): Fundamental electronic library

  • The volume is the quantitative characteristic of the space occupied by the body or substance. The volume of the body or the capacity of the vessel is determined by its shape and linear dimensions. With the concept of volume, the concept of capacity is closely connected, that is, the volume of the internal space of the vessel, the packaging box, etc.

Unit of measuring volume in Cubic meter; It is formed by derivatives of units, such as a cubic centimeter, a cubic decimeter (liter), etc. In different countries for liquid and bulk substances, various extra system units are also used - a gallon, barrel.

In the formulas for the designation of volume, the title Latin letter V is used, which is a reduction from the lat. Volume - "Volume", "Filling".

The word "volume" is also used in a figurative value for the designation of the total number or current value. For example, the "volume of demand", "memory volume", "volume of work". In the visual art, the volume is called the illusory transmission of the spatial characteristics of the artistic method depicted by artistic methods.

Volume , but, m. one. The magnitude is long, width and height of any. Bodies with closed surfaces measured in cubic units. O. Bowl. O. Rooms are 140 cubic meters. meters. O. Water increases when heated. 2. The size is dimensions. Book of a small volume. O. Capital investments in industry. || Maintenance of why From the point of view of the size, sizes, the amount of contained. O. works. O. Knowledge. Put the problem throughout.

Volume , -We , Nature, ot. Bud. BP. from Throughout.

A source: "The Explanatory Dictionary of the Russian Language" edited by D. N. Ushakov (1935-1940); (electronic version): Fundamental electronic library

volume

1. Measure occupied by the body of space, measured in cubic units

3. Three-dimensional body ◆ several Volumes Crosses, forming a polyhedron.

4. The inner part of the body ◆ It is assumed that the electron electronics is set due to the movement of electrons from the surface in volume on dislocations. V. D. Kulikov, "Conductance current in the structure of metal - dielectric - metal", 2004.10.15 // "Journal of Technical Physics" (quote from the NKry)

5. Review. tehn The same that the working volume of the piston engine of internal combustion ◆ gasoline engine Volume 1.4 liters ensures the maximum speed of 90 km / h and the stroke of 400 km. Vladimir Mosalev, "Light Combat Machines of Foreign States", 2004.08.04 // "Soldier of Good luck" (Quote from the Nc)

Phraseologisms and sustainable combinations

  • in full
  • volume of sales
  • volume of production
  • scope of work
  • Working volume

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How understands the meaning of the word segment (noun):

The meaning of the term "specific"

You can talk about two interpretations, physical and statistical:

  • In physics, it is so called the value measured in a unit of something. For example, take the room, and we calculate the amount of water vapor in it. After receiving the magnitude, and grams, we can say that the humidity here is, and the grams of water vapor to the whole room. Knowing the total amount of indoor air (b kg), we can find how much water is contained in one kilogram of the air, having learned it Specific humidity . In one kilogram of air, the room contains a / b g / kg of water vapor. Thus, the synonym for the term protrudes the word relative .
  • In the statistical sciences, the private indicator is so called relatively certain. For example, we take the annual budget of the country, which makes up 500 million, and calculate the share of sports costs. Suppose, 1 million rubles were allocated to the sport - this is 0.2% of all planned spending. Not the most weighty budget.

Formula for gravity

The mathematical description of the phenomenon of gravity was made possible thanks to numerous observations of the movement of cosmic bodies. The results of all these observations in the XVII century summarized Isaac Newton within the framework of the world of world gravity. According to this law, two bodies that have M1 and M2 masses are attracted to each other with such force F:

F = g * m1 * m2 / r2

Where R is the distance between the bodies, G is some permanent.

If this expression substitute the value of the mass of our planet and its radius, then we obtain the following mass formula in physics:

Here F is the strength of gravity, G is an acceleration with which the bodies fall on the ground near her surface.

As you know, the presence of gravity causes that all bodies have weight. Many are confused by weight and mass, believing that this is the same value. Both values ​​are really associated through the G coefficient, however, the weight is changeable (it depends on the acceleration with which the system is moving). In addition, weight is measured in Newton, and a weight in kilograms.

The scales with which a person enjoys in everyday life (mechanical, electronic) show a lot of body, but it is measured by its weight. The translation between these values ​​is only a matter of calibration of the device.

Examples of solving problems

Before proceeding with examples, it should be understood that if the data is given in kilograms and cubic centimeters, then you need to move centimeters to meters, or kilograms translate into grams. By the same principle, the remaining data must be translated - millimeters, tons and so on.

Task 1. . Find a mass of the body consisting of a substance whose density is 2350 kg / m³ and has a volume of 20 m³. We use the standard formula and with ease we find the value. m = p * v = 2 350 * 20 = 47 000 kg.

Task 2. . It is already known that the density of pure gold without impurities is 19.32 g / cm³. Find the mass of the precious chain of gold, if the volume is 3.7 cm³. We use the formula and substitute the value. P = M / V = ​​19.32 / 3.7 = 5,22162162 gr.

Task 3. . The warehouse was put metal with a density of 9250 kg / m³. The mass is 1.420 tons. It is necessary to find the volume occupied by the volume. Here you must first translate either tons per kilograms or meters in kilometers. It will be easier to use the first method. V = m / p = 1420/9250 = 0.153513514 m³.

Volumes of geometric tel

Earlier, integrals were traditionally used to determine the volume of geometric bodies. Today there are other approaches that are presented in detail in the textbooks of our corporation. In one of the webinars of the "Russian textbook", Alexey Doronin teacher spoke about the methods of determining the volume of different geometric bodies using the principle of Cavalieri and other axioms.

Definition of volume

Volume can be defined as a function VOn the set of polyhedra satisfying the following axioms:

  • Vpersists when driving.
  • VSatisfies the principle of Cavalieri.
  • If the insides of polyhedra M и Ndo not intersect, then V (m ∪ n) = V (M) + V (n) .
  • The volume of rectangular parallelepipeda V = ABC. .

Principle of Cavalieri (Italian mathematics, Galilean student). If with the intersection of two bodies with planes parallel to the same plane, in the sections of these bodies, any of the planes are figures, whose areas are treated as M: N. then the volumes of these bodies belong as M: N. .

In an open bank, the tasks of the EGE there are many tasks to work out this method of determining the volume.

Examples

Task 1. Two rectangular parallelepiped ribs emerging from one vertex are equal to 2 and 6. The volume of the parallelepiped is 48. Find the third edge of the parallelepiped coming out of the same vertex.

Task 2. Find the volume of the polyhedron shown in the figure (all dumarted corners are direct).

Task 3. Find the volume of the polyhedron shown in the figure (all dumarted corners are direct).

We will analyze how to calculate the volumes of figures studied at school.

Volume of prism

The present case is known for the base area and the height of the prism. To find the volume, we use the principle of Cavalieri. Next to Prism ( Ф2) Let's place the rectangular parallelepiped ( Ф1), at the base of which - a rectangle with the same area, as at the base of the prism. The height of the parallelepiped is the same as the inclined edge prism. Denote the third plane ( α) And consider the cross section. The cross section shows a rectangle with an area Sand, in the second case, a polygon is also with an area S. Next, calculate the formula:

V S. Osn h

Volume of pyramid

Lemma: Two triangular pyramids with equilibrium bases and equal heights areometric. We prove it using the Kawalieri principle.

Take two pyramids of the same height and conclude them between two parallel planes. α и β. Denote also the securing plane and triangles in sections. Note that the ratio of the areas of these triangles is associated directly with the ratio of the grounds.

V 1/ V. 2 = 1 V. 1 = V. 2

It is known that the volume of any pyramid is equal to one third of the product of the base area to height. This theorem is appealed quite often. However, where in the formula volume of the pyramid appears 1/3 coefficient? To understand this, take a prism and throw it on 3 triangular pyramids:

VPrism S H = 3V

Cylinder volume

Take a direct circular cylinder, which knows the radius of the base and height. Next to place the rectangular parallelepiped, at the base of which the square is. Consider:

VCyl = πh × r 2

Cone volume

The cone is best compared with the pyramid. For example, with the right quadrangular pyramid with a square at the base. Two figures with equal heights conclude in two parallel planes. Denot to the third plane, in the section we get a circle and square. Submission of similarity leads to the number π.

SF1 / S. F2. = π.

Vcone = 1/3 πr. 2 h

Bowl

The volume of the ball is one of the most difficult topics. If the previous figures can be productively disassembled in one lesson, then the ball is better to postpone the subsequent occupation.

To find the ball volume, the ball is often invited to compare with a complex geometric body, which is associated with a cone and cylinder. But you should not build a cylinder from which the cone is cut out, or like that. Take half a ball with a height Rand radius R, as well as a cone and a cylinder with similar heights and radii of bases. Let us turn to useful materials on the site "Mathematical etudes", where the volume of the ball is considered using the Archimedes weights. The cylinder is located on one side of balanced scales, the cone and half of the ball - to another.

We conclude geometric shapes in two parallel planes and look at what is obtained in the section. At the cylinder - a circle with an area πr. 2. As you know, if the insides of geometric bodies do not intersect, the volume of their association is equal to the amount of volumes. Let in the cone and half a ball the distance to the seventure plane will be x. Radius - too x. Then the area of ​​the cross section of the cone - π ∙ X. 2. Distance from the middle of the top of half a bowl to the edge of the section - R. Section area of ​​half of the ball: π (R. 2 - X. 2 ).

Notice, that: πr. 2 + πr. 2 - πr. 2 = πr. 2

VCyl = πr. 2 × R = πR 3 = 1/3 R. 3 π + V. Shara

VShara = 4/3 πr. 3

So, to find the volume of a new, not studied geometric body, you need to compare it with that body that is most like it. Numerous examples of tasks from an open bank tasks show that in work with figures it makes sense to use the presented formulas and axioms.

Basic formulas of thermodynamics and molecular physics

The last topic in the mechanics is "oscillations and waves":

Now you can safely switch to molecular physics:

We smoothly go to the category, which studies the general properties of macroscopic systems. This is thermodynamics:

Square and volume

Measure the length L, width B and the thickness T of the table cover in your laboratory (Fig. 2.1). For lengths of more than 15 cm, sufficient accuracy will give a meter (or semi-meter) ruler, graduated in mm. For example, for a table cover L = 108.0 cm long and a width of b = 92.6 cm. The meter line gives accuracy of about 0.1%, roughly 1: 1000. Square The working surface and the table covers is a = lb. Thus, a = (108.0) cm x (92.6) cm, or a = (1.08) m x (0.926) m, hence a = 10 000.8 cm 2, or a = 1,000 08 m 2. Note that as a result of determining the area A, a response containing six significant digits was obtained, which is accuracy of 0.001%, roughly 1: 1 000 000. Since the initial measurements for L and b were given 1: 1000 accuracy, then such accuracy is not true. . The answer for A should be expressed as 10,000 cm 2, or 1,000 m 2, i.e. to accuracy 1: 1000. This calculation leaves the opportunity to choose whether to use us or m. To calculate the area, it seems that the use of meters (give a number of 1,000 m) more preferably.

The symbol is the Greek letter this η. But more often still use the expression of the efficiency.

The power of the mechanism or device is equal to the work performed per unit of time. Work (A) is measured in Joules, and time in the system SI - in seconds. But it is not worth confused by the concept of power and rated power. If a power is written on the kettle 1,700 watts, this does not mean that it will give 1,700 joule in one second of water, poured into it. This power is nominal. To learn η electric kettle, you need to know the amount of heat (q), which should obtain a certain amount of water when heated on the enon number of degrees. This figure is divided into operation of the electric current, made during the heating of water.

The value A will be equal to the rated power multiplied by time in seconds. Q will be equal to the volume of water multiplied by the temperature difference on the specific heat capacity. Then we divide q to a current and get an electric kettle efficiency, approximately 80 percent. Progress does not stand still, and efficiency of various devices rises, including household appliances.

The question of why the efficiency of the device cannot be obtained through power. Nominal power is always indicated on the packaging with the equipment. It shows how much energy consumes the device from the network. But in each case it will not be possible to predict how much the energy is required to heate even one liter of water.

For example, in a cold room, part of the energy will spend on heat heating. This is due to the fact that as a result of the heat exchange, the kettle will be cooled. If, on the contrary, the room will be hot, the kettle will boil faster. That is, the efficiency in each of these cases will be different.

Relative humidity of air, the amount of heat

Saturated and unsaturated pairs

Saturated steam

When evaporated simultaneously with the transition of molecules from the liquid in steam, the reverse process occurs. Right moving above the surface of the liquid, some of the molecules that left it, returns to the liquid again.

If evaporation occurs in a closed vessel, then first the number of molecules flying out of the liquid will be greater than the number of molecules returned back into the liquid. Therefore, the pair density in the vessel will gradually increase. With an increase in the pair density, the number of molecules returning to the liquid increases. Pretty soon the number of molecules departing from the liquid will become equal to the number of steam molecules returning back into the liquid. From this point on, the number of steam molecules above the liquid will be constant. For water at room temperature, this number is approximately equal to $ 10 ^ <22> $ molecules for $ 1C $ $ 1 cm ^ 2 $ surface area. There is a so-called dynamic equilibrium between the steam and liquid.

Couples, located in dynamic equilibrium with its liquid, is called a saturated ferry.

This means that in this amount at this temperature there can be a greater number of steam.

With dynamic equilibrium, the mass of fluid in a closed vessel does not change, although the fluid continues to evaporate. Similarly, the mass of saturated steam above this liquid is also changed, although the pairs continue to condense.

Saturated steam pressure. In compressing a saturated pair, the temperature of which is maintained constant, the equilibrium will first begin to break: the density of the vapor will increase, and as a result of the gas to the liquid, more molecules will transition from the liquid than from the liquid in the gas; It will continue until the concentration of steam in the new volume becomes the same, corresponding to the concentration of saturated steam at a given temperature (and equilibrium will be restored). It is explained by the fact that the number of molecules leaving fluid per unit of time depends only on temperature.

So, the concentration of rich steam molecules at a constant temperature does not depend on its volume.

Since the gas pressure is proportional to the concentration of its molecules, the pressure of the saturated pair does not depend on the volume occupied by it. Pressure $ p_0 $ in which the liquid is in equilibrium with its ferry, called pressure of saturated steam.

When the saturated pair is compressed, its large part goes into a liquid state. The liquid occupies a smaller volume than the pairs of the same mass. As a result, the pair volume with its unchanged density decreases.

The dependence of the pressure of saturated steam on temperature. For perfect gas, the linear dependence of pressure from temperature is valid for constant volume. With reference to a saturated pair with a pressure of $ p_0 $, this dependence is expressed by equality:

Since the pressure of a saturated pair does not depend on the volume, then, therefore, it depends only on temperature.

An experimentally defined dependence $ P_0 (T) $ differs from the dependence of $ p_0 = nkt $ for perfect gas. With increasing temperature, the pressure of a saturated steam increases faster than the pressure of the perfect gas (the $ AV $ curve section). This becomes especially obvious if you have been from a point of $ A $ (dotted straight). It happens because when the fluid is heated, part of it turns into steam, and the pair density increases.

Therefore, according to the formula $ p_0 = nkt $, The pressure of the saturated steam is growing not only as a result of increasing the temperature of the fluid, but also due to an increase in the concentration of molecules (density) of steam. The main difference in the behavior of the ideal gas and a saturated pair is to change the mass of steam when the temperature changes at a constant volume (in a closed vessel) or when the volume is changed at a constant temperature. With the perfect gas, nothing like this may occur (the ICT of the ideal gas does not provide for the phase transition of gas into the liquid).

After evaporation of the entire fluid, the behavior of the pair will correspond to the behavior of the perfect gas (section of the $ $ $ curve).

Unsaturated par

If there may be further evaporation of this fluid in the space containing a pair of any liquid, then the steam in this space is unsaturated .

Couple, not in a state of equilibrium with its liquid, is called unsaturated.

Unsaturated pairs can turn into a liquid with simple compression. As soon as this transformation began, couples in equilibrium with liquid becomes saturated.

Air humidity

Air humidity is the content of water vapor.

The atmospheric air surrounding us due to continuous evaporation of water from the surface of the oceans, seas, reservoirs, wet soil and plants always contains water vapors. The more water vapor is in a certain amount of air, the closer steam to saturation state. On the other hand, the higher the air temperature, the greater the amount of water vapor is required for saturation.

Depending on the number of water vapors that are at a given temperature in the atmosphere, the air is of varying degrees of humidity.

Quantitative valuation of moisture

In order to quantify air humidity, use, in particular, with concepts Absolute и relative humidity.

Absolute humidity is the number of grams of water vapor contained in $ 1m ^ 3 $ air under these conditions, i.e. it is a density of a water vapor $ p $, expressed in g / $ m ^ $ 3.

The relative air humidity $ φ $ is the ratio of the absolute humidity of the air $ p $ to the density of $ p_0 $ saturated steam at the same temperature.

Relative humidity is expressed as a percentage:

The concentration of the steam is associated with pressure ($ p_0 = nkt $), so relative humidity can be defined as a percentage partial pressure $ p $ vapor in the air to the pressure of $ p_0 $ saturated steam at the same temperature:

Under partial pressure Understand the pressure of the water vapor, which he would produce, if all other gases in the atmospheric air were absent.

If the wet air is cooling, then at a certain temperature, the steam located in it can be brought to saturation. In the further cooling of the water vapor will begin to condense in the form of dew.

Dew point

The dew point is the temperature to which the air should cool so that the water vapor in it reaches the saturation state at constant pressure and this humidity. When the dew point is reached in the air or on the items with which it comes into contacts, the condensation of water vapor begins. The dew point can be calculated by the temperature and humidity of the air or determined directly condensation hygrometer. For relative humidity $ φ = 100% $ dew point coincides with air temperature. For $ φ T_1 $ and, therefore, $ Q> 0 $. When cooling the body $ T_2

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How to find a volume in physics

The volume numely characterizes some area of ​​space with specified boundaries. In several sections of mathematics, it is calculated in the form of boundaries and dimensions or by cross section and coordinates. When they talk about the physical formula for calculating the volume, they usually mean calculations for other body parameters - density and mass.

How to find a volume in physics

Instruction

Learn the density (ρ) of the material constituting the physical body, the volume of which must be calculated. The density is one of the two characteristics of the object involved in the formula for calculating the volume. If we are talking about real objects, the average density is used in the calculations, since absolutely

homogeneous

Physical body in real conditions is difficult. It will definitely be unevenly distributed at least microscopic emptiness or inclusions of foreign materials. Take into account when determining this parameter and

Temperature

- what it is higher, the less the density of the substance, since

Heating increases

Distance between It

Molecules

.

The second parameter that is needed to calculate the volume - the mass (m) of the body under consideration. This value will be determined, as a rule, according to the results of the interaction of an object with other objects or the gravitational fields created by them. Most often have to deal with a mass expressed through interaction with the force of attraction of the Earth - weighing the body. Ways to determine this value for relatively small objects are simple - they need to simply weigh.

To calculate the volume (V) of the body, divide the parameter defined in the second step - to the parameter obtained in the first step - the density: v = m / ρ.

In practical calculations, the calculator volume can be used in practical calculations. It is convenient because it does not require to look for somewhere else the density of the desired material and enter it into the calculator - in the form there is a drop-down list with the list of the most frequently used in the calculations of the materials. By selecting the required string in it, enter the weight in the "Mass" field, and in the "Calculation Accuracy" field, set the number of decimal values ​​that must be present as a result of calculations. The volume in liters and cubic meters can be found in the table below. In addition, just in case, the radius of the sphere and the side of the cube will be given, which should correspond to the volume of the selected substance.

Sources:

  • Calculator volume
  • Volume of physics formula

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