Charles's law definition and formula. Gas laws

1. Who and when the experiment was carried out, what was its purpose

The first gas law was discovered by Robert Boyle and published in 1660 in his work “New Experiments Concerning an Air Spring.” R. Boyle, based on a carefully designed quantitative experiment, proved that “the elasticity [pressure] of a gas is inversely proportional to its volume.” During his research, he attempted to quantitatively study the dependence of the volume of compressed gas on temperature. However, R. Boyle did not receive exact data confirming this dependence.

Research on the expansion of air when heated was carried out by G. Amonton. Later, similar experiments were carried out by A. Volta, D. Dalton, J. Priestley, T. Saussure and others.

It is believed that the first satisfactory measurements in the study thermal expansion gases were obtained in 1801 by the English physicist and chemist John Dalton (1766–1844). He discovered that oxygen, hydrogen and carbon dioxide behaved the same when heated.

Based on the results obtained, D. Dalton formulates the conclusion in an extremely cautious manner: “In general, I do not see a sufficient reason to prevent us from concluding that all “elastic” gases at the same pressure expand equally when heated.”

A similar conclusion was reached by J. L. Gay-Lussac in 1802. But his statement was more definite than that of D. Dalton. Apparently, this is why the law on the thermal expansion of gases is called not after D. Dalton, but after J. L. Gay-Lussac.

The device used by Gay-Lussac is shown in Fig. 2. The gas, thoroughly dried, is in a can. There is a drop of mercury in the tube that traps the gas. The tubes are located horizontally, so there is no change in pressure during expansion.

Fifteen years earlier than Gay-Lussac (in 1787), research on this issue was undertaken, without any publication, by the French physicist Jacques Charles (1746–1823). Charles found that oxygen, nitrogen, carbon dioxide and air expand equally in the temperature range between 0 and 100 ºС. Gay-Lussac knew about his colleague’s work and insisted that the second gas law be named after Jacques Alexandre César Charles. It should be noted that in some countries, including Russia, this law is still known as Gay-Lussac's law. In publications on the history of science, the priority of the discovery of the third gas law - the law of changes in gas pressure depending on temperature - is usually not discussed. This dependence, as well as the dependence of gas volume on temperature, was studied by many scientists who studied the properties of gases in the 17th–18th centuries. The history of the discovery of the law of thermal expansion of gases is connected with the history of the invention and improvement of thermometers.

The first instrument for measuring “heat” and “cold” in the body is the air thermoscope of G. Galileo (1597). The essence of the experience that served as the impetus for the creation of the thermoscope was as follows. A small flask, the size of an egg, with a long and thin neck like a wheat stalk, lowered into a bowl of water, is warmed with hands. If you remove your hands, the water from the bowl, as the air in the flask cools, will begin to rise into the neck. Benedetto Castelli, a student of G. Galileo, writes in 1638: “The above-mentioned Signor Galileo used this effect to make an instrument for determining the degree of heat and cold.”

Evangelista Torricelli converted G. Galileo's air thermoscope into a liquid (alcohol) thermometer. E. Torricelli's thermometer - the so-called "Florentine thermometer" - was very convenient to use and therefore received universal recognition in the 17th century. Thermometers of this type were introduced in England by R. Boyle, and they quickly spread to France.

The improvement of G. Galileo's air thermometer was carried out by G. Amonton, a French physicist, member of the Paris Academy of Sciences (1699). In 1702, he designed a thermometer, very similar in its concept to the modern gas thermometer. G. Amonton's thermometer was a U-shaped glass tube, the shorter elbow of which ended in a reservoir containing air. Mercury was poured into the long elbow in the amount necessary to maintain a constant volume of air in the tank. The air temperature in the tank was determined by the height of the mercury column.

It is interesting to note that, working with this tool, it was Amonton who found directly proportional dependence between temperature and gas pressure and came to the concept absolute zero, which according to his data corresponded to a temperature of –239.5 °C (1703).

2. Instruments and materials necessary for the experiment, circuit diagram pilot plant

The setup for experiments to study the dependence of gas pressure on temperature at constant volume was quite complex.

Let's look at the circuit diagram experimental setup to study the dependence of gas pressure on temperature at constant volume.

The main part of such an installation is a large flask in which the gas was located. The flask is placed in a vessel with water. The change in gas pressure can be judged by the readings of a mercury manometer connected to the flask. The gas temperature is measured using a mercury thermometer.

J. Charles studied the dependence of pressure on temperature for the following gases: oxygen, nitrogen, carbon dioxide and air.

3. Procedure for conducting the experiment

Having filled the flask with melting ice, Charles measured the pressure corresponding to a temperature of 0 ºС. Then the temperature of the water in the large vessel changed, which led to a change in the height of the mercury column in the manometer. By heating water in a vessel surrounding the flask, Charles noted the temperature of the gas with a thermometer and the corresponding pressure with a manometer. During the experiment, the influence of a number of factors distorted the course of the experiment. Firstly, due to heating, the flask with gas partially changed its volume; accordingly, strict constancy of the volume of the gas under study was not ensured. Secondly, the gas located in the so-called “harmful space” (in the thin tube leading to the pressure gauge) was not heated in the same way as in the flask. Thirdly, the presence of impurities in the gas (in particular, condensing vapors) led to the fact that part of the components that made up the gas turned into liquid state

. Other factors were also at play. Attempts by scientists to exclude harmful effects side effects

on the course of the experiment and led, as a rule, to a complication of the design of the installation.

4. Main results of the experiment

The experiments of J. Charles showed the following results. The increase in gas pressure of a certain mass when heated by 1 ºС was certain part

The value α p is called the temperature coefficient of pressure. Having studied a number of gases, Charles obtained for them approximately same value temperature coefficient of pressure, namely a value equal to approximately 1/273 ºС –1.

Thus, the pressure of a certain mass of gas, when heated by 1 ºС with a constant volume, increases by 1/273 of the pressure that this mass of gas had at 0 ºС.

5. Main results of the experiment

IN modern formulation This law is as follows.

Mathematically, J. Charles’s law can be written as:

where P 0 is the gas pressure at T = T 0 = 273.15 K (that is, at a temperature of 0 ° C). A coefficient equal to 1/273.15 K –1 is called the temperature pressure coefficient.

The figure shows the dependence of the pressure of a given mass of gas on its temperature. For different temperatures gas location of the dependence curve on coordinate plane various. Isochores depicting the dependence of P on T for a gas that obeys Charles’s law are straight lines, located higher on the graph, the smaller the volume.

Charles's law is valid only for ideal gas. It is applicable with to a certain extent accuracy to real gases at low pressures and low temperatures (for example, atmospheric air, combustion products in gas engines, etc.)

An explanation for the law established by Charles can be given from the standpoint of molecular kinetic concepts of the structure of matter.

From point of view molecular theory There are two possible reasons for the increase in pressure of a given gas: firstly, the number of impacts of molecules per unit time per unit area may increase; secondly, it is possible to increase the impulse transmitted when one molecule hits the vessel wall. Both reasons require an increase in the speed of molecules (while the volume of a given mass of gas remains unchanged). From here it becomes clear that an increase in gas temperature as a macro-characteristic corresponds to an increase in the speed of random movement of molecules as a characteristic of the microcosm.

At very high pressures the interaction between gas molecules increases and deviations from the linear Charles law are observed.

Charles's law is derived as special case from the Mendeleev–Clapeyron equation:

where k = 1.38 J/K is Boltzmann’s constant.

Ideal gas isoprocesses– processes in which one of the parameters remains unchanged.

1. Isochoric process . Charles's law. V = const.

Isochoric process called a process that occurs when constant volume V. The behavior of the gas in this isochoric process obeys Charles' law :

At constant volume and constant values ​​of gas mass and its molar mass, the ratio of gas pressure to its absolute temperature remains constant: P/T= const.

Graph of an isochoric process on PV-the diagram is called isochore . It is useful to know the graph of an isochoric process on RT- And VT-diagrams (Fig. 1.6).

Isochore equation: Where P 0 is pressure at 0 °C, α is the temperature coefficient of gas pressure equal to 1/273 deg -1. A graph of such a dependence onРt

-diagram has the form shown in Figure 1.7.

2. Rice. 1.7 Isobaric process. Gay-Lussac's law. R

= const. An isobaric process is a process that occurs at constant pressure R . The behavior of a gas during an isobaric process obeys:

Gay-Lussac's law At constant pressure and constant values ​​of the mass of both the gas and its molar mass, the ratio of the volume of the gas to its absolute temperature remains constant:= const.

V/T VT-the diagram is called Graph of an isobaric process on isobar PV- And . It is useful to know the graphs of the isobaric process on RT

-diagrams (Fig. 1.8).

Rice. 1.8

Isobar equation: Where α =1/273 deg -1 - temperature coefficient volumetric expansion . A graph of such a dependence on Vt

diagram has the form shown in Figure 1.9.

3. Rice. 1.9 Isothermal process. Boyle-Mariotte law.= const.

T Isothermal process is a process that occurs when constant temperature

T. The behavior of an ideal gas during an isothermal process obeys

Boyle–Mariotte law: At a constant temperature and constant values ​​of the mass of the gas and its molar mass, the product of the volume of the gas and its pressure remains constant:= const.

PV Schedule isothermal process PV-the diagram is called on isotherm VT- And . It is useful to know the graphs of the isobaric process on. It is useful to know the graphs of an isothermal process on

-diagrams (Fig. 1.10).

Rice. 1.10

4. Isotherm equation: Adiabatic process

(isentropic):

5. An adiabatic process is a thermodynamic process that occurs without heat exchange with the environment. Polytropic process. A process in which the heat capacity of a gas remains constant. Polytropic process – general case

6. all of the above processes. Avogadro's law. At the same pressures and the same temperatures, in equal volumes various ideal gases contained same number molecules In one mall various substances contains N A =6.02·10 23

7. molecules (Avogadro's number). Dalton's law.

(1.4.6)

Partial pressure Pn is the pressure that a given gas would exert if it alone occupied the entire volume.

At , gas mixture pressure.

At constant pressure, the volume of a gas is proportional to its temperature.

One of the pioneers of aeronautics, Jacques Alexandre César Charles, came to science as a result of his passion for building hot air balloons - large balloons, filled with heated air, which had just appeared then. I have spoken with modern balloon pilots, and they claim that their open gas burner design, developed by Charles more than two centuries ago, has not undergone fundamental changes and is still used today. It's not surprising that scientific interests Charles lay in the field of studying the properties of gases, therefore, no. Charles formulated the law that bears his name in 1787 after a series of experiments with oxygen, nitrogen, hydrogen and carbon dioxide.

To understand the meaning of Charles's law, imagine a gas as a collection of rapidly moving and colliding molecules. The pressure of a gas is determined by the impacts of molecules on the walls of the container: the more impacts, the higher the pressure. For example, the air molecules in the room you are in exert a pressure of 101,325 pascals (or 1 bar, if we're talking about about meteorology).

To understand Charles's law, imagine the air inside balloon. At a constant temperature, the air in the balloon will expand or contract until the pressure produced by its molecules reaches 101,325 pascals and equals atmospheric pressure. In other words, until for every blow of an air molecule from the outside, directed into the ball, there will be a similar blow of an air molecule, directed from the inside of the ball outward. If you lower the temperature of the air in the ball (for example, by placing it in a large refrigerator), the molecules inside the ball will begin to move more slowly, hitting the walls of the ball less energetically from the inside. The molecules of the outside air will then put more pressure on the ball, compressing it, as a result the volume of gas inside the ball will decrease. This will happen until the increase in gas density compensates for the decreased temperature, and then equilibrium will be established again.

Charles's law, along with other gas laws, formed the basis of the equation of state of an ideal gas, which describes the relationship between the pressure, volume and temperature of a gas with the amount of substance.

Jacques Alexandre César Charles, 1746-1823

French physicist, chemist, engineer and aeronaut. Born in Beaugency. In his youth he served as an official in the Ministry of Finance in Paris. Having become interested in aeronautics, he developed hot air balloons of a modern design, the lifting force of which is due to the expansion of air heated by a burner inside the balloon. He was one of the first to fill Balloons hydrogen (which is many times lighter than air and provides significantly greater lift than hot air), thereby setting records for lift height (more than 3,000 m) and flight range (43 km). It was aeronautics that made Charles interested in studying the properties of gases.

Charles's Law or Gay-Lussac's second law - one of the basic gas laws that describes the relationship between pressure and temperature for an ideal gas. Experimentally, the dependence of gas pressure on temperature at constant volume was established in 1787 by Charles and refined by Gay-Lussac in 1802.

Ambiguity of terminology[ | ]

In Russian- and English-language scientific literature There are some differences in the names of the laws associated with the name of Gay-Lussac. These differences are presented in the following table:

Statement of the law[ | ]

The formulation of Charles's law is as follows:

The pressure of a gas of a fixed mass and a fixed volume is directly proportional to the absolute temperature of the gas.

Simply put, if the temperature of a gas increases, then its pressure also increases, if the mass and volume of the gas remain unchanged. The law is especially simple mathematical form, if the temperature is measured by absolute scale, for example, in kelvins. Mathematically, the law is written as follows:

This law is true because temperature is a measure of the average kinetic energy of a substance. If kinetic energy gas increases, its particles collide with the walls of the vessel faster, thereby creating higher pressure.

To compare the same substance at two different conditions, the law can be written as:

(\displaystyle (\frac (P_(1))(T_(1)))=(\frac (P_(2))(T_(2)))\qquad \mathrm (or) \qquad (P_(1) )(T_(2))=(P_(2))(T_(1)).) Amonton's law on pressure and temperature: the law of pressure described above should in fact be attributed to Guillaume Amonton, who in early XVIII

century (more precisely between 1700 and 1702) discovered that the pressure of a fixed mass of gas maintained at a constant volume is proportional to its temperature. Amonton discovered this during the construction of an "air thermometer". Calling this law Gay-Lussac's law is simply incorrect, since Gay-Lussac studied the relationship between volume and temperature, not pressure and temperature.

Ambiguity of terminology

Charles's law was known as Charles and Gay-Lussac's law because Gay-Lussac published it in 1802 using Charles's largely unpublished data since 1787. Gay-Lussac's law, Charles's law and Boyle's law - Mariotte all together form the unified gas law. In combination with

Statement of the law

The formulation of Charles's law is as follows:

The pressure of a gas of a fixed mass and a fixed volume is directly proportional to the absolute temperature of the gas.

Gay Lussac's law

Simply put, if the temperature of a gas increases, then its pressure also increases, if the mass and volume of the gas remain unchanged. The law has a particularly simple mathematical form if the temperature is measured on an absolute scale, for example, in degrees Kelvin. Mathematically, the law is written as follows:

see also

Notes

Links

• Literature Castka, Joseph F.; Metcalfe, H. Clark; Davis, Raymond E.; Williams, John E.
• Modern Chemistry. - Holt, Rinehart and Winston, 2002. - ISBN 0-03-056537-5 Guch, Ian
• The Complete Idiot's Guide to Chemistry. - Alpha, Penguin Group Inc., 2003. - ISBN 1-59257-101-8 Mascetta, Joseph A. How to Prepare for the

SAT II Chemistry. - Barron's, 1998. - ISBN 0-7641-0331-8

Wikimedia Foundation.

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