Boyle's law of respiration - Mariotte. Gas Laws Mathematical Expression of Boyle Marriott's Law

Let us now turn to a more detailed study of the question of how the pressure of a certain mass of gas changes if its temperature remains unchanged and only the volume of the gas changes. We have already found out what isothermal the process is carried out under the condition that the temperature of the bodies surrounding the gas is constant, and the volume of the gas changes so slowly that the temperature of the gas at any moment of the process does not differ from the temperature of the surrounding bodies. Thus, we pose the question: how are volume and pressure related to each other during an isothermal change in the state of a gas? Daily experience teaches us that when the volume of a certain mass of gas decreases, its pressure increases. Examples include the increase in elasticity when inflating a soccer ball, bicycle or car tire. The question arises: how exactly does the pressure of a gas increase with a decrease in volume, if the temperature of the gas remains unchanged?

The answer to this question was given by studies carried out in the 17th century by the English physicist and chemist Robert Boyle (1627-1691) and the French physicist Edem Mariotte (1620-1684).

Experiments that establish the relationship between the volume and pressure of a gas can be reproduced: on a vertical stand , equipped with divisions, there are glass tubes BUT and AT, connected by a rubber tube C. Mercury is poured into the tubes. Tube B is open at the top, tube A has a stopcock. Let us close this faucet, thus locking a certain mass of air in the tube BUT. As long as we don't move the tubes, the mercury level in both tubes is the same. This means that the pressure of the air trapped in the tube BUT, the same as the ambient air pressure.

Now let's slowly pick up the phone AT. We will see that the mercury in both tubes will rise, but not in the same way: in the tube AT the level of mercury will always be higher than in A. If, however, tube B is lowered, then the level of mercury in both knees decreases, but in the tube AT decrease more than BUT. The volume of air trapped in the tube BUT, can be counted from the divisions of the tube BUT. The pressure of this air will differ from the atmospheric one by the pressure of the mercury column, the height of which is equal to the difference between the levels of mercury in tubes A and B. At. pick up the phone AT the pressure of the mercury column is added to the atmospheric pressure. The volume of air in A decreases. When dropping the tube AT the level of mercury in it is lower than in A, and the pressure of the mercury column is subtracted from atmospheric pressure; air volume in A

increases accordingly. Comparing the pressure and volume of air locked in tube A obtained in this way, we will be convinced that when the volume of a certain mass of air increases by a certain number of times, its pressure decreases by the same amount, and vice versa. The temperature of the air in the tube during our experiments can be considered unchanged. Similar experiments can be carried out with other gases. The results are the same. So,

the pressure of a certain mass of gas at a constant temperature is inversely proportional to the volume of gas (Boyle-Mariotte law). For rarefied gases, the Boyle-Mariotte law is satisfied to a high degree

accuracy. For gases that are highly compressed or cooled, noticeable deviations from this law are found. The formula expressing the Boyle-Mariotte law.

The statement of Boyle's law - Mariotte is as follows:

In mathematical form, this statement is written as a formula

$pV=C,$

where $p$ - gas pressure; $V$ is the volume of gas, and $C$ - a constant value under the specified conditions. In general, the value $C$ determined by the chemical nature, mass and temperature of the gas.

Obviously, if the index 1 designate the quantities related to the initial state of the gas, and the index 2 - to the final one, then the above formula can be written in the form

$p_1 V_1 = p_2 V_2$ .

From what has been said and the above formulas, the form of the dependence of gas pressure on its volume in an isothermal process follows:

$p=\frac (C)(V).$

This dependence is another, equivalent to the first, expression of the content of the Boyle-Mariotte law. She means that

The pressure of a certain mass of gas at a constant temperature is inversely proportional to its volume.

Then the relationship between the initial and final states of the gas participating in the isothermal process can be expressed as:

$\frac (p_1)(p_2) = \frac (V_2)(V_1).$

It should be noted that the applicability of this and the above formula, which relates the initial and final pressures and volumes of gas to each other, is not limited to the case of isothermal processes. The formulas remain valid even in those cases when the temperature changes during the process, but as a result of the process, the final temperature is equal to the initial one.

It is important to clarify that this law is valid only in cases where the gas under consideration can be considered ideal. In particular, the Boyle-Mariotte law is fulfilled with high accuracy in relation to rarefied gases. If the gas is highly compressed, then significant deviations from this law are observed.

Consequences

The Boyle-Mariotte law states that the pressure of a gas in an isothermal process is inversely proportional to the volume occupied by the gas. If we take into account that the density of the gas is also inversely proportional to the volume it occupies, then we will come to the conclusion:

In an isothermal process, the pressure of a gas changes in direct proportion to its density.

\beta_T=\frac(1)(p).

Thus, we come to the conclusion:

The isothermal compressibility coefficient of an ideal gas is equal to the reciprocal of its pressure.

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Notes

Petrushevsky F.F.// Encyclopedic Dictionary of Brockhaus and Efron
// Physical Encyclopedia / Ch. ed. A. M. Prokhorov. - M .: Soviet Encyclopedia, 1988. - T. 1. - S. 221-222. - 704 p. - 100,000 copies
Sivukhin D.V. General course of physics. - M .: Fizmatlit, 2005. - T. II. Thermodynamics and molecular physics. - S. 21-22. - 544 p. - ISBN 5-9221-0601-5.
Elementary textbook of physics / Ed. G. S. Landsberg. - M .: Nauka, 1985. - T. I. Mechanics. Heat. Molecular physics. - S. 430. - 608 p.
Kikoin A. K., Kikoin I. K. Molecular physics. - M .: Nauka, 1976. - S. 35-36.
At a constant mass.
Livshits L. D.// Physical Encyclopedia / Ch. ed. A. M. Prokhorov. - M .: Great Russian Encyclopedia, 1994. - T. 4. - S. 492-493. - 704 p. - 40,000 copies. - ISBN 5-85270-087-8.

Literature

Petrushevsky F.F.// Encyclopedic Dictionary of Brockhaus and Efron: in 86 volumes (82 volumes and 4 additional). - St. Petersburg. , 1890-1907.

An excerpt characterizing Boyle's Law - Mariotte

“She’s the best,” a rough female voice was heard in response, and after that Marya Dmitrievna entered the room.
All the young ladies and even the ladies, except for the oldest ones, stood up. Marya Dmitrievna stopped at the door and, from the height of her corpulent body, holding high her fifty-year-old head with gray curls, looked around the guests and, as if rolling up, unhurriedly straightened the wide sleeves of her dress. Marya Dmitrievna always spoke Russian.
“Dear birthday girl with children,” she said in her loud, thick voice that overwhelms all other sounds. “Are you an old sinner,” she turned to the count, who was kissing her hand, “do you miss tea in Moscow?” Where to run the dogs? But what, father, to do, this is how these birds will grow up ... - She pointed to the girls. - Whether you like it or not, you need to look for suitors.
- Well, what, my Cossack? (Marya Dmitrievna called Natasha a Cossack) - she said, caressing Natasha with her hand, who approached her hand without fear and cheerfully. - I know that the potion is a girl, but I love it.
From her huge reticule, she took out yakhon earrings with pears and, giving them to Natasha, who was beaming and blushing on her birthday, immediately turned away from her and turned to Pierre.
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And she rolled up her sleeves menacingly even higher.
Pierre came up, naively looking at her through his glasses.
"Come, come, dear!" I told your father the truth alone, when he happened to be, and then God commands you.
She paused. Everyone was silent, waiting for what was to come, and feeling that there was only a preface.
- Okay, nothing to say! good boy! ... The father lies on the bed, and he amuses himself, he puts the quarter on a bear on horseback. Shame on you, dad, shame on you! Better to go to war.
She turned away and offered her hand to the count, who could hardly help laughing.
- Well, well, to the table, I have tea, is it time? said Marya Dmitrievna.
The count went ahead with Marya Dmitrievna; then the countess, who was led by a hussar colonel, the right person with whom Nikolai was supposed to catch up with the regiment. Anna Mikhailovna is with Shinshin. Berg offered his hand to Vera. Smiling Julie Karagina went with Nikolai to the table. Behind them came other couples, stretching across the hall, and behind them all alone, children, tutors and governesses. The waiters stirred, chairs rattled, music played in the choir stalls, and the guests settled in. The sounds of the count's home music were replaced by the sounds of knives and forks, the voices of guests, the quiet footsteps of waiters.
At one end of the table, the countess sat at the head. On the right is Marya Dmitrievna, on the left is Anna Mikhailovna and other guests. At the other end sat a count, on the left a hussar colonel, on the right Shinshin and other male guests. On one side of the long table, older youth: Vera next to Berg, Pierre next to Boris; on the other hand, children, tutors and governesses. From behind the crystal, bottles and vases of fruit, the count glanced at his wife and her high cap with blue ribbons and diligently poured wine to his neighbors, not forgetting himself. The Countess, also, because of the pineapples, not forgetting her duties as a hostess, threw significant glances at her husband, whose bald head and face, it seemed to her, were sharply distinguished by their redness from gray hair. There was a regular babble at the ladies' end; voices were heard louder and louder on the male, especially the hussar colonel, who ate and drank so much, blushing more and more that the count already set him as an example to other guests. Berg, with a gentle smile, spoke to Vera about the fact that love is a feeling not earthly, but heavenly. Boris called his new friend Pierre the guests who were at the table and exchanged glances with Natasha, who was sitting opposite him. Pierre spoke little, looked at new faces and ate a lot. Starting from two soups, from which he chose a la tortue, [turtle,] and kulebyaki, and up to grouse, he did not miss a single dish and not a single wine, which the butler in a bottle wrapped in a napkin mysteriously protruded from his neighbor’s shoulder, saying or “drey Madeira, or Hungarian, or Rhine wine. He substituted the first of the four crystal glasses with the count's monogram, which stood in front of each device, and drank with pleasure, looking more and more pleasantly at the guests. Natasha, who was sitting opposite him, looked at Boris, as girls of thirteen look at the boy with whom they had just kissed for the first time and with whom they are in love. This same look of hers sometimes turned to Pierre, and under the look of this funny, lively girl he wanted to laugh himself, not knowing why.
Nikolai was sitting far away from Sonya, next to Julie Karagina, and again, with the same involuntary smile, he spoke something to her. Sonya smiled grandly, but apparently she was tormented by jealousy: she turned pale, then blushed, and with all her might listened to what Nikolai and Julie were saying to each other. The governess looked around uneasily, as if preparing herself for a rebuff, if anyone thought of offending the children. The German tutor tried to memorize the categories of foods, desserts and wines in order to describe everything in detail in a letter to his family in Germany, and was very offended by the fact that the butler, with a bottle wrapped in a napkin, surrounded him. The German frowned, tried to show that he did not want to receive this wine, but was offended because no one wanted to understand that he needed wine not to quench his thirst, not out of greed, but out of conscientious curiosity.

At the male end of the table the conversation became more and more lively. The colonel said that the manifesto declaring war had already been published in Petersburg, and that the copy, which he himself had seen, had now been delivered by courier to the commander-in-chief.

According to boyle's law- marriotte, at constant temperature the volume gas inversely proportional to pressure.

This means that as the pressure on the gas increases, its volume decreases, and vice versa. For a constant amount of gas Boyle's Law - Mariotte can also be interpreted as follows: at a constant temperature, the product of pressure and volume is a constant value. This is expressed as a formula:

P x V \u003d K, where P is the absolute pressure, V is the volume; K is a constant.

If P and V change, then P 1 x V 1 \u003d K and P 2 x V 2 \u003d K.

Combining the two equations will give P 1 x V 1 = P 2 x V 2 .

If a fixed amount of gas is pumped into a rigid container, such as a scuba cylinder, then, since the volume of the cylinder remains unchanged, it will determine the pressure of the gas inside it. If the same amount of gas fills an elastic container, such as a balloon. it will expand until the pressure of the gas inside it equals the pressure of the environment. In this case, the pressure determines the volume of the container.

The effect of increasing pressure with depth diving on the example of a plastic bottle. As the pressure on a gas increases, its volume decreases, and vice versa.

At sea level, the pressure is 1 bar. At a depth of 10 meters, the pressure doubles to 2 bar and then increases by 1 bar for every 10 meters of immersion. Imagine an inverted glass bottle without a cork, with air inside. When the bottle is immersed to a depth of 10 meters, where the pressure is 2 bar. the air inside it will be compressed to half its original volume. At a depth of 20 meters, the pressure will be 3 bar. and the air will be compressed to a third of its original volume. At 30 meters deep, where the pressure rises to 4 bar. the volume of air will be only a quarter of the original.

If a pressure and the volume of a gas are inversely proportional, the pressure and density are directly proportional. As the pressure of a gas increases and its volume decreases, the distance between the gas molecules decreases, and the gas becomes denser. At twice atmospheric pressure, a given volume of gas is twice as dense as air at the surface of the water, and so on. Therefore, at depth, divers use up their available air supply faster. A full breath of air at twice atmospheric pressure contains twice as many air molecules as air at the surface. Therefore, at a pressure of 3 atmospheres, the balloon will last only a third of the time during which a person could use this balloon on the surface.

diver must breathe air, the pressure of which is equal to the pressure of the surrounding aquatic environment. Only then, regardless of the depth of immersion, the expansion of air to the normal volume of the lungs will be ensured. The air regulator is a valve system that reduces the pressure of compressed air in a cylinder to water pressure at the level of the diver's lungs. divers don't want to waste the air in their tank, so the regulator is designed that way. to supply air only when needed. Hence the other name - "demand valve". that is, a valve that operates on demand.

At every immersion divers carry various items of equipment containing the gas, including buoyancy control devices, cylinders, masks, wet and dry neoprene wetsuits made from a material containing tiny air bubbles. Our body also has gas-filled cavities: sinuses, ears. stomach and lungs. With the exception of rigid cylinders, all gas-filled cavities contract on descent and expand on ascent. When ascending to the surface, divers must relieve the expanding air in their lungs, equalize the pressure in their ears and sinuses to avoid pain and tissue damage, called barotrauma. (This does not apply to decompression stops - they are a separate topic.)

It is believed that the expansion of gases in the diver's body is especially intense in the last 10 meters of ascent, which is why at this stage you should rise slowly, gradually exhaling air.

Composition of sea water

Among the chemical compounds that give sea water its salty taste is dominated by table salt (sodium chloride). On average, sea water contains about 3% salt, although this figure can vary from 1% in the polar seas to 5% in closed ones, such as the Mediterranean and Red. The salt obtained by evaporating sea water is 77.76% sodium chloride, 10.88% magnesium chloride, 4.74% magnesium sulfate, 3.60% calcium sulfate, 2 46% from potassium chloride, 0.22% from magnesium bromide and 0.34% from calcium carbonate.

The basic laws of ideal gases are used in technical thermodynamics to solve a number of engineering and technical problems in the process of developing design and technological documentation for aviation equipment, aircraft engines; their manufacture and operation.

These laws were originally obtained experimentally. Subsequently, they were derived from the molecular-kinetic theory of the structure of bodies.

Boyle's Law - Mariotte establishes the dependence of the volume of an ideal gas on pressure at a constant temperature. This dependence was deduced by the English chemist and physicist R. Boyle in 1662 long before the advent of the kinetic theory of gas. Regardless of Boyle in 1676, the same law was discovered by E. Mariotte. Law of Robert Boyle (1627 - 1691), English chemist and physicist who established this law in 1662, and Edme Mariotte (1620 - 1684), French physicist who established this law in 1676: the product of the volume of a given mass of an ideal gas and its pressure is constant at constant temperature or.

The law is called Boyle-Mariotte and states that at constant temperature, the pressure of a gas is inversely proportional to its volume.

Let at a constant temperature of a certain mass of gas we have:

V 1 - volume of gas at pressure R 1 ;

V 2 - volume of gas at pressure R 2 .

Then, according to the law, we can write

Substituting in this equation the value of the specific volume and taking the mass of this gas t= 1kg, we get

p 1 v 1 =p 2 v 2 or pv= const .(5)

The density of a gas is the reciprocal of its specific volume:

then equation (4) takes the form

i.e., the densities of gases are directly proportional to their absolute pressures. Equation (5) can be considered as a new expression of the Boyle-Mariotte law, which can be formulated as follows: the product of pressure and the specific volume of a certain mass of the same ideal gas for its various states, but at the same temperature, is a constant value.

This law can be easily obtained from the basic equation of the kinetic theory of gases. Replacing in equation (2) the number of molecules per unit volume by the ratio N/V (V is the volume of a given mass of gas, N is the number of molecules in the volume) we get

Since for a given mass of gas the quantities N and β constant, then at constant temperature T=const for an arbitrary amount of gas, the Boyle–Mariotte equation will have the form

pV = const, (7)

and for 1 kg of gas

pv = const.

Depict graphically in the coordinate system R – v change in the state of the gas.

For example, the pressure of a given mass of gas with a volume of 1 m 3 is 98 kPa, then, using equation (7), we determine the pressure of a gas with a volume of 2 m 3

Continuing the calculations, we get the following data: V(m 3) is equal to 1; 2; 3; 4; 5; 6; respectively R(kPa) equals 98; 49; 32.7; 24.5; 19.6; 16.3. Based on these data, we build a graph (Fig. 1).

Rice. 1. Dependence of the pressure of an ideal gas on the volume at

constant temperature

The resulting curve is a hyperbola, obtained at a constant temperature, is called an isotherm, and the process occurring at a constant temperature is called isothermal. The Boyle-Mariotte law is approximate and at very high pressures and low temperatures is unacceptable for thermal engineering calculations.

Gay–L u s s a ka law determines the dependence of the volume of an ideal gas on temperature at constant pressure. (The law of Joseph Louis Gay-Lussac (1778 - 1850), a French chemist and physicist who first established this law in 1802: the volume of a given mass of ideal gas at constant pressure increases linearly with increasing temperature, i.e , where is the specific volume at; β is the volume expansion coefficient equal to 1/273.16 per 1 o C.) The law was established experimentally in 1802 by the French physicist and chemist Joseph Louis Gay-Lussac, whose name is named. Investigating the thermal expansion of gases experimentally, Gay-Lussac discovered that at a constant pressure, the volumes of all gases increase almost equally when heated, that is, with an increase in temperature by 1 ° C, the volume of a certain mass of gas increases by 1/273 of the volume that this mass gas occupied at 0°C.

The increase in volume during heating by 1 ° C by the same value is not accidental, but, as it were, is a consequence of the Boyle-Mariotte law. First, the gas is heated at a constant volume by 1 ° C, its pressure increases by 1/273 of the initial one. Then the gas expands at a constant temperature, and its pressure decreases to the initial one, and the volume increases by the same factor. Denoting the volume of a certain mass of gas at 0°C through V 0 , and at temperature t°C through V t Let's write the law as follows:

Gay-Lussac's law can also be represented graphically.

Rice. 2. Dependence of the volume of an ideal gas on temperature at a constant

pressure

Using equation (8) and assuming the temperature is 0°C, 273°C, 546°C, we calculate the volume of gas, respectively, V 0 , 2V 0 , 3V 0 . Let us plot the gas temperatures on the abscissa axis in some conditional scale (Fig. 2), and the gas volumes corresponding to these temperatures along the ordinate axis. Connecting the obtained points on the graph, we get a straight line, which is a graph of the dependence of the volume of an ideal gas on temperature at constant pressure. Such a line is called isobar, and the process proceeding at constant pressure - isobaric.

Let us turn once again to the graph of the change in the volume of gas from temperature. Let's continue the straight line to the intersection, with the x-axis. The point of intersection will correspond to absolute zero.

Let us assume that in equation (8) the value V t= 0, then we have:

but since V 0 ≠ 0, hence, whence t= – 273°C. But - 273°C=0K, which was required to be proved.

We represent the Gay-Lussac equation in the form:

Remembering that 273+ t=T, and 273 K \u003d 0 ° C, we get:

Substituting in equation (9) the value of the specific volume and taking t\u003d 1 kg, we get:

Relation (10) expresses the Gay-Lussac law, which can be formulated as follows: at constant pressure, the specific volumes of identical masses of the same ideal gas are directly proportional to its absolute temperatures. As can be seen from equation (10), the Gay-Lussac law states that that the quotient of dividing the specific volume of a given mass of gas by its absolute temperature is a constant value at a given constant pressure.

The equation expressing the Gay-Lussac law, in general, has the form

and can be obtained from the basic equation of the kinetic theory of gases. Equation (6) can be represented as

at p=const we obtain equation (11). Gay-Lussac's law is widely used in engineering. So, on the basis of the law of volumetric expansion of gases, an ideal gas thermometer was built to measure temperatures in the range from 1 to 1400 K.

Charles' law establishes the dependence of the pressure of a given mass of gas on temperature at a constant volume. the pressure of an ideal gas of constant mass and volume increases linearly when heated, that is, where R o - pressure at t= 0°C.

Charles determined that when heated in a constant volume, the pressure of all gases increases almost equally, i.e. when the temperature rises by 1 ° C, the pressure of any gas increases exactly by 1/273 of the pressure that this mass of gas had at 0 ° C. Let us denote the pressure of a certain mass of gas in a vessel at 0°C through R 0 , and at temperature t° through p t . When the temperature rises by 1°C, the pressure increases by, and when the temperature increases by t°Cpressure increases by. pressure at temperature t°C equal to initial plus pressure increase or

Formula (12) allows you to calculate the pressure at any temperature if the pressure at 0°C is known. In engineering calculations, an equation (Charles' law) is often used, which is easily obtained from relation (12).

Because, and 273 + t = T or 273 K = 0°C = T 0

At constant specific volume, the absolute pressures of an ideal gas are directly proportional to the absolute temperatures. By interchanging the middle terms of the proportion, we get

Equation (14) is an expression of Charles's law in a general form. This equation can be easily derived from formula (6)

At V=const we obtain the general equation of Charles's law (14).

To construct a graph of the dependence of a given mass of gas on temperature at a constant volume, we use equation (13). Let, for example, at a temperature of 273 K=0°C, the pressure of a certain mass of gas is 98 kPa. According to the equation, the pressure at a temperature of 373, 473, 573 ° C, respectively, will be 137 kPa (1.4 kgf / cm 2), 172 kPa (1.76 kgf / cm 2), 207 kPa (2.12 kgf / cm 2). Based on these data, we build a graph (Fig. 3). The resulting straight line is called isochore, and the process proceeding at constant volume is called isochoric.

Rice. 3. Dependence of gas pressure on temperature at constant volume

Boyle's law - Mariotte

Boyle's Law - Mariotte- one of the fundamental gas laws, discovered in 1662 by Robert Boyle and independently rediscovered by Edme Mariotte in 1676. Describes the behavior of a gas in an isothermal process. The law is a consequence of the Clapeyron equation.

1 Wording
2 Consequences
3 See also
4 Notes
5 Literature

Wording

Boyle's law - Mariotte is as follows:

At constant temperature and mass of a gas, the product of the pressure of a gas and its volume is constant.

In mathematical form, this statement is written as a formula

where is the gas pressure; is the volume of gas, and is a constant value under the specified conditions. In general, the value is determined by the chemical nature, mass and temperature of the gas.

Obviously, if index 1 denotes the quantities related to the initial state of the gas, and index 2 - to the final state, then the above formula can be written as

. From what has been said and the above formulas, the form of the dependence of gas pressure on its volume in an isothermal process follows:

This dependence is another, equivalent to the first, expression of the content of the Boyle-Mariotte law. She means that

The pressure of a certain mass of gas at a constant temperature is inversely proportional to its volume.

Then the relationship between the initial and final states of the gas participating in the isothermal process can be expressed as:

It should be noted that the applicability of this and the above formula, which relates the initial and final pressures and volumes of gas to each other, is not limited to the case of isothermal processes. The formulas remain valid even in those cases when the temperature changes during the process, but as a result of the process, the final temperature is equal to the initial one.

Boyle's law - Mariotte, Charles's law and Gay-Lussac's law, supplemented by Avogadro's law, are a sufficient basis for obtaining the ideal gas equation of state.

Consequences

In an isothermal process, the pressure of a gas changes in direct proportion to its density.

It is known that compressibility, that is, the ability of a gas to change its volume under pressure, is characterized by a compressibility factor. In the case of an isothermal process, one speaks of an isothermal compressibility coefficient, which is determined by the formula

where the index T means that the partial derivative is taken at a constant temperature. Substituting in this formula the expression for the relationship between pressure and volume from the Boyle-Mariotte law, we get:

Thus, we come to the conclusion:

The isothermal compressibility coefficient of an ideal gas is equal to the reciprocal of its pressure.

Notes

Boyle - Mariotte's law // Physical Encyclopedia / Ch. ed. A. M. Prokhorov. - M.: Soviet Encyclopedia, 1988. - T. 1. - S. 221-222. - 704 p. - 100,000 copies.
Sivukhin DV General course of physics. - M.: Fizmatlit, 2005. - T. II. Thermodynamics and molecular physics. - S. 21-22. - 544 p. - ISBN 5-9221-0601-5.
1 2 Elementary textbook of physics / Ed. G. S. Landsberg. - M.: Nauka, 1985. - T. I. Mechanics. Heat. Molecular physics. - S. 430. - 608 p.
1 2 3 Kikoin A.K., Kikoin I.K. Molecular physics. - M.: Nauka, 1976. - S. 35-36.
At a constant mass.
Livshits L. D. Compressibility // Physical Encyclopedia / Ch. ed. A. M. Prokhorov. - M.: Great Russian Encyclopedia, 1994. - T. 4. - S. 492-493. - 704 p. - 40,000 copies.
ISBN 5-85270-087-8.

Literature

Petrushevsky F. F. Boyle-Mariotte law // Encyclopedic Dictionary of Brockhaus and Efron: in 86 volumes (82 volumes and 4 additional). - St. Petersburg, 1890-1907.

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Boyle-Mariotte law

The quantitative relationship between the volume and pressure of a gas was first established by Robert Boyle in 1662. * Boyle-Mariotte's law states that at a constant temperature, the volume of a gas is inversely proportional to its pressure.

This law applies to any fixed amount of gas. As can be seen from fig. 3.2, its graphical representation may be different. The graph on the left shows that at low pressure, the volume of a fixed amount of gas is large.

The volume of a gas decreases as its pressure increases. Mathematically, this is written like this:

However, Boyle-Mariotte's law is usually written in the form

Such a record allows, for example, knowing the initial gas volume V1 and its pressure p to calculate the pressure p2 in the new volume V2.

Gay-Lussac's law (Charles' law)

In 1787, Charles showed that at constant pressure, the volume of a gas changes (in proportion to its temperature. This dependence is presented in graphical form in Fig. 3.3, from which it can be seen that the volume of a gas is linearly related to its temperature. In mathematical form, this dependence is expressed as follows :

Charles' law is often written in a different form:

V1IT1 = V2T1(2)

Charles' law was improved by J. Gay-Lussac, who in 1802 found that the volume of a gas, when its temperature changes by 1°C, changes by 1/273 of the volume that it occupied at 0°C.

It follows that if we take an arbitrary volume of any gas at 0°C and at constant pressure reduce its temperature by 273°C, then the final volume will be equal to zero. This corresponds to a temperature of -273°C, or 0 K. This temperature is called absolute zero. In fact, it cannot be achieved. On fig.

Figure 3.3 shows how the extrapolation of plots of gas volume versus temperature leads to zero volume at 0 K.

Absolute zero is, strictly speaking, unattainable. However, under laboratory conditions, it is possible to achieve temperatures that differ from absolute zero by only 0.001 K. At such temperatures, the random motions of molecules practically stop. This results in amazing properties.

For example, metals cooled to temperatures close to absolute zero lose their electrical resistance almost completely and become superconducting*. An example of substances with other unusual low-temperature properties is helium.

At temperatures close to absolute zero, helium loses its viscosity and becomes superfluid.

* In 1987, substances were discovered (ceramics sintered from oxides of lanthanide elements, barium and copper) that become superconducting at relatively high temperatures, on the order of 100 K (-173 °C). These "high-temperature" superconductors open up great prospects in technology.- Approx. transl.

Main laboratory equipment is the desktop on which all experimental work is carried out.

Every laboratory should have good ventilation. A fume hood is required, in which all work is carried out using foul-smelling or toxic compounds, as well as burning organic substances in crucibles.

In a special fume hood, in which work related to heating is not carried out, volatile, harmful or foul-smelling substances (liquid bromine, concentrated nitric and hydrochloric acids, etc.) are stored.

), as well as flammable substances (carbon disulfide, ether, benzene, etc.).

The laboratory needs water supply, sewerage, technical current, gas wiring and water heaters. It is also desirable to have a compressed air supply, vacuum line, hot water and steam supply.

If there is no special supply, water heaters of various systems are used to produce hot water.

By means of these apparatuses, heated by electricity or gas, a jet of hot water at a temperature of almost 100°C can be quickly obtained.

The laboratory must have installations for distillation (or demineralization) of water, since it is impossible to work in the laboratory without distilled or demineralized water. In cases where obtaining distilled water is difficult or impossible, commercial distilled water is used.

There must be clay jars with a capacity of 10-15 liters near work tables and water sinks for draining unnecessary solutions, reagents, etc., as well as baskets for broken glass, paper and other dry garbage.

In addition to working tables, the laboratory should have a desk where all notebooks and notes are stored, and, if necessary, a title table. There should be high stools or chairs near the work tables.

Analytical balances and instruments requiring a stationary installation (electrometric, optical, etc.) are placed in a separate room associated with the laboratory, and a special weighing room should be allocated for analytical balances. It is desirable that the weighing room be located with windows to the north. This is important because the balance must not be exposed to sunlight (“Scales and Weighing”).

In the laboratory, you must also have the most necessary reference books, manuals and textbooks, since often during work there is a need for tone or other information.

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Chemical glassware used in laboratories can be divided into a number of groups. According to the purpose, the dishes can be divided into general-purpose, special-purpose and measured dishes. According to the material - for dishes made of plain glass, special glass, quartz.

To the group. general purpose items include those items that should always be in laboratories and without which most work cannot be carried out. These are: test tubes, simple and separating funnels, glasses, flat-bottomed flasks, crystallizers, conical flasks (Erlenmeyer), Bunsen flasks, refrigerators, retorts, flasks for distilled water, tees, taps.

The special purpose group includes those items that are used for any one purpose, for example: the Kipp apparatus, the Sok-rally apparatus, the Kjeldahl apparatus, reflux flasks, Wulff flasks, Tishchenko flasks, pycnometers, hydrometers, Drexel flasks, Kali apparatus , carbon dioxide tester, round bottom flasks, special refrigerators, molecular weight tester, melting and boiling point testers, etc.

Volumetric utensils include: graduated cylinders and beakers, pipettes, burettes and volumetric flasks.

To get started, we suggest watching the following video, where the main types of chemical glassware are briefly and easily considered.

Lesson 25

Lesson archive › Basic laws of chemistry

Lesson 25 " Boyle-Mariotte law» from the course « Chemistry for dummies» consider the law relating pressure and volume of gas, as well as graphs of pressure versus volume and volume versus pressure. Let me remind you that in the last lesson "Gas pressure" we examined the device and principle of operation of a mercury barometer, and also gave a definition of pressure and considered its units of measurement.

Robert Boyle(1627-1691), to whom we owe the first practically correct definition of a chemical element (we will learn in Chapter 6), was also interested in the phenomena occurring in vessels with rarefied air.

In inventing vacuum pumps for pumping air out of closed containers, he drew attention to a property familiar to anyone who had ever inflated a football chamber or carefully squeezed a balloon: the more air in a closed container is compressed, the more it resists compression.

Boyle called this property " springiness» air and measured it using a simple device shown in fig. 3.2, a and b.

Boyle sealed some air with mercury at the closed end of the curved tube (Fig. 3-2, a) and then compressed this air, gradually adding mercury to the open end of the tube (Fig. 3-2, b).

The pressure experienced by the air in the closed part of the tube is equal to the sum of atmospheric pressure and the pressure of a mercury column of height h (h is the height by which the level of mercury at the open end of the tube exceeds the level of mercury at the closed end). The pressure and volume measurement data obtained by Boyle are given in Table. 3-1.

Although Boyle did not take special measures to maintain a constant temperature of the gas, it seems that in his experiments it changed only slightly. However, Boyle noticed that the heat from the candle flame caused significant changes in the properties of the air.

Analysis of data on the pressure and volume of air during its compression

Table 3-1, which contains Boyle's experimental data on the relationship between pressure and volume for atmospheric air, is located under the spoiler.

After the researcher receives data similar to those given in Table. 3-1, he is trying to find a mathematical equation that relates two mutually dependent quantities that he measured.

One way to get such an equation is to graphically plot different powers of one quantity against another, hoping to get a straight line graph.

The general equation of a straight line is:

where x and y are related variables, and a and b are constant numbers. If b is zero, a straight line passes through the origin.

On fig. 3-3 show various ways of graphical representation of data for pressure P and volume V, given in table. 3-1.

Graphs of P versus 1/K and V versus 1/P are straight lines passing through the origin.

The plot of log P versus log V is also a negatively sloped straight line whose angle tangent is -1. All three of these plots lead to the equivalent equations:

P \u003d a / V (3-3a)
V = a / P (3-3b)

lg V \u003d lg a - lg P (3-3c)

Each of these equations is one of the variants Boyle-Mariotte law, which is usually formulated as follows: for a given number of moles of a gas, its pressure is proportional to its volume, provided that the temperature of the gas remains constant.

By the way, you probably wondered why the Boyle-Mariotte law is called a double name. This happened because this law, independently of Robert Boyle, who discovered it in 1662, was rediscovered by Edme Mariotte in 1676. That's it.

When the relationship between two measured quantities is as simple as in this case, it can also be established numerically.

If each value of pressure P is multiplied by the corresponding value of volume V, it is easy to verify that all products for a given gas sample at constant temperature are approximately the same (see Table 3-1). Thus, one can write that

Equation (3-3g) describes the hyperbolic relationship between the values of P and V (see Fig. 3-3, a). To verify that the graph of the dependence of P on V, built according to experimental data, really corresponds to a hyperbola, we will construct an additional graph of the dependence of the product P V on P and make sure that it is a horizontal straight line (see Fig. 3-3,e) .

Boyle found that for a given amount of any gas at a constant temperature, the relationship between pressure P and volume V is quite satisfactorily described by the relation

P V = const (at constant T and n) (3-4)

Formula from the Boyle-Mariotte law

To compare the volumes and pressures of the same gas sample under different conditions (but at a constant temperature), it is convenient to represent boyle-mariotte law in the following formula:

where indices 1 and 2 correspond to two different conditions.

Example 4 Plastic food bags delivered to the Colorado Plateau (see Example 3) often burst because the air in them expands as it rises from sea level to a height of 2500 m, under conditions of reduced atmospheric pressure.

If we assume that 100 cm3 of air is contained inside the bag at atmospheric pressure corresponding to sea level, what volume should this air occupy at the same temperature on the Colorado Plateau? (Assume that puckered bags are used to deliver products that do not restrict air expansion; the missing data should be taken from example 3.)

Decision
We will use Boyle's law in the form of equation (3-5), where index 1 will refer to conditions at sea level, and index 2 to conditions at an altitude of 2500 m above sea level. Then P1 = 1.000 atm, V1 = 100 cm3, P2 = 0.750 atm, and V2 should be calculated. So,

Boyle's law of respiration - Mariotte. Gas Laws Mathematical Expression of Boyle Marriott's Law

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Composition of sea water

Boyle's law - Mariotte

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Boyle-Mariotte law

Page 3

Lesson 25

Analysis of data on the pressure and volume of air during its compression

Formula from the Boyle-Mariotte law