To describe the state of a gas, it is enough to set three macroscopic parameters - volume V, pressure p and temperature T. Changing one of these parameters causes a change in the others. If volume, pressure and temperature change simultaneously, then it is difficult to establish any patterns experimentally. It is easier to first consider a gas of constant mass ( m= const), fix the value of one of the macro parameters ( V, p or T) and consider the change in the other two.

Processes in which one of the parameters p, V or Τ remains constant for a given mass of gas is called isoprocesses.

isos means "equal" in Greek.

The laws describing isoprocesses in an ideal gas were discovered experimentally.

Isothermal process

Isothermal process is an isoprocess that occurs at a constant temperature: Τ = const.

therme - warmth.

The law was experimentally discovered independently of each other by the English chemist and physicist Robert Boyle (1662) and the French physicist Edme Mariotte (1676).

Law of isothermal process(Boyle-Mariotte): for a given mass of gas at a constant temperature, the product of pressure and volume is a constant:

\(~p \cdot V = \operatorname(const)\) or for two states \(~p_1 \cdot V_1 = p_2 \cdot V_2 .\)

To carry out an isothermal process, a vessel filled with gas must be brought into contact with a thermostat.

A thermostat is a device for maintaining a constant temperature. See wikipedia for more details.

An isothermal process can be approximately considered the process slow compression or expansion of gas in a vessel with a piston. The thermostat in this case is the environment.

Isobaric process

Isobaric process is an isoprocess that occurs at constant pressure: p= const.

baros - heaviness, weight.

The work of J. Charles was published after the discovery of J. Gay-Lussac. But the isobaric process in Russian textbooks is called Gay-Lussac's law, in Belarusian - Charles's law.

Law of isobaric process: for a given mass of gas at constant pressure, the ratio of volume to absolute temperature is a constant:

\(~\dfrac(V)(T) = \operatorname(const),\) or \(~\dfrac(V_1)(T_1) = \dfrac(V_2)(T_2) .\)

This law can be written in terms of temperature t, measured on the Celsius scale\[~V = V_0 \cdot (1 + \alpha \cdot t),\] where V 0 - volume of gas at 0 °C, α = 1/273 K -1 - temperature coefficient volumetric expansion.

Experience shows that at low densities the temperature coefficient of volumetric expansion does not depend on the type of gas, i.e. is the same for all gases).

An isobaric process can be achieved using a cylinder with a weightless piston.

Isochoric process

Isochoric process is an isoprocess that occurs at constant volume: V= const.

chora - occupied space, volume.

The law was experimentally studied independently by the French physicists Jacques Charles (1787) and Joseph Gay-Lussac (1802).

The isochoric process is called Charles's law in Russian textbooks, and Gay-Lussac's law in Belarusian textbooks.

Law of isochoric process: for a given mass of gas at a constant volume, the ratio of pressure to absolute temperature is a constant value:

\(~\dfrac(p)(T) = \operatorname(const)\), or \(~\dfrac(p_1)(T_1) = \dfrac(p_2)(T_2) .\)

If temperature is measured on the Celsius scale, then Gay-Lussac's law will be written in the form\[~p = p_0 \cdot (1 + \alpha \cdot t),\] where p 0 - gas pressure at 0 °C, α - temperature coefficient of pressure, which turned out to be the same for all gases: α = 1/273 K -1.

An isochoric process can be obtained in a cylinder that does not change its volume with a given temperature change.

Thorough experimental verification modern methods showed that the equation of state of an ideal gas and the resulting laws of Boyle-Mariotte, Gay-Lussac and Charles quite accurately describe the behavior of real gases at low pressures and not too low temperatures.

A little math

Graph of a function y(x), Where a, b And With- constant values:

y = a⋅x- a straight line passing through the origin of coordinates (Fig. 1, a);
y = c- straight, perpendicular to the axis y and passing through the point with coordinate y = c(Fig. 1, b);
\(~y = \dfrac(b)(x) \) is a hyperbola (Fig. 1, c).

Rice. 1

Isoprocess graphs

Since we are considering three macro parameters p, T And V, then three coordinate systems are possible: ( p, V), (V, Τ ), (p, T).

Graphs of the dependence between the parameters of a given mass at a constant temperature are called isotherms.

Let us consider two isothermal processes with temperatures T 1 and T 2 (T 2 > T 1). In coordinates where there is a temperature axis (( V, T) And ( p, T T, and passing through the points T 1 and T 2 (Fig. 2, a, b).

p, V). For an isothermal process \(~p \cdot V = \operatorname(const)\). Let us denote this constant by the letter z 1. Then

\(~p \cdot V = z_1\) or \(~p = \dfrac(z_1)(V)\).

The graph of this function is a hyperbola (Fig. 2, c).

Rice. 2

Graphs of the relationship between gas parameters at constant gas mass and pressure are called isobars.

Let us consider two isobaric processes with pressures p 1 and p 2 (p 2 > p 1). In coordinates where there is a pressure axis (( p, T) And ( p, V)), the graphs will be straight lines perpendicular to the axis p, and passing through the points p 1 and p 2 (Fig. 3, a, b).

Let's determine the type of graph in the axes ( V, T). For an isobaric process \(~\dfrac(V)(T) = \operatorname(const)\). Let us denote this constant by the letter z 2. Then

\(~\dfrac(V)(T) = z_2\) or \(~V = z_2 \cdot T\).

The graph of this function is a straight line passing through the origin of coordinates (Fig. 3, c).

Rice. 3

Graphs of the relationship between gas parameters at constant gas mass and constant volume are called isochores.

Let us consider two isochoric processes with volumes V 1 and V 2 (V 2 > V 1). In coordinates where there is a volume axis (( V, T) And ( p, V)), the graphs will be straight lines perpendicular to the axis V, and passing through the points V 1 and V 2 (Fig. 4, a, b).

Let's determine the type of graph in the axes ( p, T). For an isochoric process \(~\dfrac(p)(T) = \operatorname(const)\). Let us denote this constant by the letter z 3. Then

\(~\dfrac(p)(T) = z_3\) or \(~p = z_3 \cdot T\).

The graph of this function is a straight line passing through the origin of coordinates (Fig. 4, c).

Rice. 4

All graphs of isoprocesses are straight lines (exception, hyperbola in the axes p(V)). These lines pass either through zero or perpendicular to one of the axes.
Since the gas pressure, its volume and temperature cannot be equal to zero, when approaching zero values graph lines are shown as dotted lines.

Ideal gas equation of state

In isoprocesses, two parameters changed while the third value remained constant. But there may be cases when three parameters change at once. For example, when air heated at the surface of the Earth rises, it expands, its pressure decreases and the temperature decreases.

Equation relating temperature T, pressure p and volume V for a given mass of an ideal gas is called gas equation of state.

This equation was derived experimentally, but can be derived from the basic MKT equation:

\(~p = n \cdot k \cdot T.\)

By definition, gas concentration

\(~n = \dfrac NV,\)

Where N- number of molecules. Then

\(~p = \dfrac NV \cdot k \cdot T \Rightarrow \dfrac(p \cdot V)(T) = k \cdot N . \qquad (1)\)

With a constant mass of a gas, the number of molecules in it is constant and the product \(~k \cdot N = \operatorname(const).\) Consequently,

\(~\dfrac(p \cdot V)(T) = \operatorname(const)\) or for two states \(~\dfrac(p_1 \cdot V_1)(T_1) = \dfrac(p_2 \cdot V_2)( T_2) .\qquad (2)\)

Relationship (2) is the equation of state of an ideal gas. They call him Clapeyron's equation. It is used in cases where the mass of gas and its chemical composition do not change and it is necessary to compare the two states of the gas.

Clapeyron-Mendeleev equation

In equation (1), the number of molecules N can be expressed through Avogadro’s constant \(~N = \dfrac mM \cdot N_A\), where m- gas mass, Μ - its molar mass. Then we get \(~\dfrac(p \cdot V)(T) = \dfrac mM \cdot k \cdot N_A \Rightarrow\)

\(~p \cdot V = \dfrac mM \cdot R \cdot T . \qquad (3)\)

Here \(~R = k \cdot N_A\) is the universal gas constant, equal to

R= 1.38·10 -23 J/K · 6.02·10 23 mol -1 = 8.31 J/(mol·K).

Equation (3) is also the equation of state of an ideal gas. In this form it was first written down by the Russian scientist D.I. Mendeleev, which is why it is called Clapeyron-Mendeleev equation. It is valid for any mass of gas and relates the parameters of one state of the gas.

Avogadro's and Dalton's laws

Two consequences follow from the equation of state:

From formula (1) we obtain \(~N = \dfrac(p \cdot V)(k \cdot T)\), which shows that if different gases occupy equal volumes at the same temperatures and pressures, then the number N their molecules are also the same, i.e. follows established empirically Avogadro's law: at equal pressures and temperatures, equal volumes of any gases contain the same number of molecules.
Let there be a mixture of gases in a vessel, each of which, in the absence of others, exerts a corresponding pressure p 1 , p 2 , ... (partial pressures gases). Let us write the equation of state for each gas:
\(~p_1 \cdot V = N_1 \cdot k\cdot T, p_2 \cdot V = N_2 \cdot k \cdot T, \ldots\)
and add them up:
\(~p_1+ p_2 + \ldots = \dfrac((N_1+ N_2 + \ldots) \cdot k \cdot T)(V) = \dfrac(N \cdot k \cdot T)(V),\)
Where N 1 + N 2 + ... = N- the number of molecules of a gas mixture. But \(~\dfrac(N \cdot k \cdot T)(V) = p\) .
Hence, p = p 1 + p 2 + ..., i.e. the pressure of a mixture of gases is equal to the sum of the partial pressures of each gas- This Dalton's law, discovered by him experimentally in 1801.

Literature

Aksenovich L. A. Physics in high school: Theory. Assignments. Tests: Textbook. benefits for institutions providing general education. environment, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsiya i vyhavanne, 2004. - P. 143-146.

Isobaric process

Isoprocess graphs in various systems coordinates

Isobaric process(ancient Greek ισος, isos - “same” + βαρος, baros - “weight”) - the process of changing the state of a thermodynamic system at constant pressure ()

The dependence of gas volume on temperature at constant pressure was experimentally studied in 1802 by Joseph Louis Gay-Lussac. Gay-Lussac's law: At constant pressure and constant values of the mass of gas and its molar mass, the ratio of the gas volume to its absolute temperature remains constant: V/T = const.

Isochoric process

Isochoric process(from the Greek chorus - occupied space) - the process of changing the state of a thermodynamic system at constant volume (). For ideal gases, the isochoric process is described by Charles' law: for a given mass of gas at constant volume, pressure is directly proportional to temperature:

The line depicting an isochoric process on a diagram is called an isochore.

It is also worth pointing out that the energy supplied to the gas is spent on changing the internal energy, that is, Q = 3* ν*R*T/2=3*V*ΔP, where R is the universal gas constant, ν is the number of moles in the gas, T is the temperature in Kelvin , V volume of gas, ΔP increment of pressure change. and the line depicting the isochoric process on the diagram, in the P(T) axes, should be extended and connected with a dotted line to the origin of coordinates, since misunderstandings may arise.

Isothermal process

Isothermal process(from the Greek “thermos” - warm, hot) - the process of changing the state of a thermodynamic system at a constant temperature ()(). The isothermal process is described by the 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: PV = const.

Isoentropic process

Isoentropic process- the process of changing the state of a thermodynamic system at constant entropy (). For example, a reversible adiabatic process is isentropic: in such a process there is no heat exchange with environment. An ideal gas in such a process is described by the following equation:

where is the adiabatic index, determined by the type of gas.

Wikimedia Foundation. 2010.

See what “Isoprocesses” are in other dictionaries:

Isoprocesses are thermodynamic processes during which mass and one more of physical quantities state parameters: pressure, volume or temperature remains unchanged. Thus, constant pressure corresponds to an isobaric process, volume is isochoric... Wikipedia

Molecular kinetic theory (abbreviated as MKT) is a theory that considers the structure of matter from the point of view of three main approximately correct provisions: all bodies consist of particles whose size can be neglected: atoms, molecules and ions; particles... ...Wikipedia

- (abbreviated MKT) a theory that considers the structure of matter from the point of view of three main approximately correct provisions: all bodies consist of particles whose size can be neglected: atoms, molecules and ions; particles are in continuous... ... Wikipedia

Books

Statistical forecasting of the deformation-strength characteristics of structural materials, G. Pluvinazh, V. T. Sapunov, This book presents new method, which offers a general methodology for predicting the characteristics of kinetic processes, common for metal and polymer materials. Method… Category: Textbooks for universities Publisher:

Topic: ISOPROCESSES AND THEIR GRAPHS. LAWS OF IDEAL GASES.

Educational tasks

Didactic purpose

Teach students to apply the Clayperon-Mendeleev equation to special cases of measuring processes in gases.

Give the concept of isoprocess, formulas of gas laws and graphs of the dependence of variable parameters in various coordinate axes of these parameters for different isoprocesses.

Educational purpose

To teach how to apply the cause-and-effect category of materialistic dialectics when explaining changes in gas pressure with changes in volume and temperature from the point of view of molecular kinetic theory.

Basic knowledge and skills

Be able to set the parameters of the initial, intermediate and final states of the gas, functional dependencies in gas processes and solve problems to find unknown parameters.

Build and analyze graphs of isoprocesses in gas.

Sequence of presentation of new material

Repeat previously studied material on the dependence of gas pressure on concentration and velocities forward motion molecules

Entering the gas equation of state with variable parameters: mass, volume, pressure and temperature.

Equation of state of a gas with its mass unchanged.

The concept of isoprocesses in gases. Definition and their types.

Isothermal process. Boyle-Marriott law.

Isobaric process. Gay-Lussac's law.

Isochoric process. Charles's law.

Equipment

Variable volume cylinder; demonstration pressure gauge; rubber tube; a glass flask with a stopper through which an L-shaped glass tube with a drop of water is passed; electric stove; thermometer; vessel with water.

Demonstrations

The relationship between the volume and pressure of a gas at constant temperature (isothermal process), the dependence of gas volume on temperature at constant pressure (isobaric process), the dependence of gas pressure on temperature at constant volume (isochoric process). All demonstrations are carried out to show the qualitative relationship between variable gas parameters.

Motivation cognitive activity students

In technology, processes are often encountered when a change in the state of a gas occurs at one constant parameter or small changes in this parameter are neglected. In this case, it is very important to know how the isoprocess proceeds.

Lesson plan

Testing students' knowledge, skills and abilities

Cards for oral questioning of students

Card 1

Derive the Clayperon-Mendeleev equation for one mole of gas.

What is the relationship between the molar gas constant, Avogadro's constant and Boltzmann's constant?

Determine the root mean square speed of movement of an oxygen molecule if it produces a pressure of 2 ∙ 10 5 Pa at a molecular concentration of 4 ∙ 10 25 m –3. Answer. ν = 530 m/s.

Card 2

Derive the Clayperon-Mendeleev equation for any mass of gas.

How does gas pressure depend on temperature at a constant concentration of molecules? Answer. p = n0kT. Pressure is directly proportional to the thermodynamic temperature of the gas.

How many gas molecules are in a vessel with a capacity of 138 liters at a temperature of 27 o C and a pressure of 6 ∙ 10 5 Pa? Answer. n = 2 ∙ 10 25 .

Card 3

Card 4

1) What is physical meaning Boltzmann constant and molar gas constant? What are they equal to in SI?

2) Why does the pressure of a real gas depend on the type of gas itself?

3) The temperature of the plasma ions in the center of the star is 10 6 K. Determine the average kinetic energy of each ion of this plasma. Answer: Ē k = 2.07∙10 -16 J.

Learning new material

1. Conduct an introductory conversation with the following questions:

1) What does the basic equation of the molecular kinetic theory of gas express?

2) What does the gas pressure on the walls of the vessel depend on?

3) What formula is used to calculate the concentration of gas molecules?

4) Explain from the point of view of molecular kinetic theory the dependence of gas pressure on the concentration of molecules and the speed of their movement?

2. Equation of state of a gas with variable parameters of mass, volume, pressure and temperature. Let the parameters of the initial (one) state of the gas be m 1, p 1, V 1 and T 1, and the parameters of the final (other) state m 2, p 2, V 2 and T 2. Let us write the Clayperon-Mendeleev equations for each state of the gas:

P 1 V 1 = RT; p 2 V 2 = RT 2 .

Dividing term by term, we get:

Solve the problem:

A certain mass of gas at a pressure of 3∙10 5 Pa and a temperature of 300 K. Then ⅜ of the gas contained in the cylinder was released, while its temperature dropped to 240 K. At what pressure is the gas remaining in the cylinder?

Answer: p 2 = 2∙10 5 Pa.

3. Equation of state of a gas at constant mass. If, when the state of a gas changes, its mass does not change, then the equation takes the form:

(Clapeyron equation).

Solve the problem:

A certain mass of gas at a pressure of 3∙10 5 Pa and a temperature of 300 K occupies a volume of 20 m 3. Determine the volume of gas under normal conditions. ANSWER: V 0 = 54.6 m 3 .

4. The concept of isoprocesses in gases. The transition of a given mass of gas from one state to another at one constant parameter is called isoprocess. There are three such isoprocesses: isometric (T = const), isobaric (p = const) and isochoric (V = const).

5. Isometric process. Demonstration of the relationship between the volume and pressure of a gas mass at a constant temperature. From the Clayperon equation has p 1 V 1 = p 2 V 2, or in general view pV = const. Let us formulate the Boyle-Mariotte law: at a constant mass of a gas and a constant temperature, the product of the volume of a gas and its pressure is a constant value.

We construct isotherms in the V, p axes for the same mass of gas at different temperatures. As the temperature increases, the gas pressure increases, and therefore the isotherm corresponding to a higher temperature T2 is located above the isotherm corresponding to a lower temperature T1 (Fig. 1).

rice. 1

The gas isotherm expresses the inversely proportional relationship between the volume and pressure of the gas.

Solve problems:

1) In a vessel with a capacity of 0.5 m 3 there is gas under a pressure of 4∙10 5 Pa. What volume will this gas occupy at a pressure of 2.5∙10 5 Pa? Answer: V 2 = 0.8 m 3.

2) Construct isotherms in the coordinate axes T, p and T, V.

Dependence of gas density on pressure during an isothermal process. Transforms the Clayperon-Mendeleev equation to the form p = mRT/(VM) = pRT/M. During an isothermal process, the gas density changes in direct proportion to its pressure: p 1 /p 2 = p 1 /p 2.

6. Isobaric process. Demonstration of the dependence of gas volume on temperature at constant pressure. From the Clapeyron equation we have V 1 V 2 = T 1 / T 2. We formulate Gay-Lussac's law: at a constant mass of gas at a constant V, the ratio of gas volumes is directly proportional to their thermodynamic temperatures.

Different pressures correspond to different isobars. As p increases, the volume of gas at a constant temperature decreases, so the isobar corresponding to a higher p 2 lies below the isobar corresponding to a lower p 1 (Fig. 2)

Fig 2

Solve problems:

1) Gas at a temperature of 27 o C occupies a volume of 600 cm 3. What V will this gas occupy at a temperature of 377 o C and constant pressure? ANSWER: 1300 cm3.

2) Construct isobars in the coordinate axes T, V; V, p and T, p.

7. Isochoric process. Demonstrate the dependence of gas pressure on temperature at constant volume. From the Clapeyron equation we have p 1 /p 2 = T 1 /T 2. We formulate Charles's law: at a constant mass of gas and a constant V, the gas pressure ratio is directly proportional to the ratio of their thermodynamic temperatures. We construct an isochore in the T, p axes using two characteristic points (0,0) and (T 0, p 0). Different isochores correspond to different volumes. With an increase in V of a gas at a constant temperature, its pressure decreases, therefore the isochore corresponding to a large V 2 lies below the isochore corresponding to a smaller V 1 (Fig. 3)

Rice. 3

To consolidate, solve problems:

1) The gas is in a cylinder at a temperature of 250 K and a pressure of 8∙10 5 Pa. Determine the gas pressure in the cylinder at a temperature of 350 K. O t. 11.2∙10 5 Pa.

2) Construct isochores in the coordinate axes T, p; T, V and V, p.

Homework: Material gas laws

In the XVII – 19th centuries experimental laws of ideal gases were formulated. Let us briefly recall them.

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 a constant volume and constant values of the 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 the pressure at 0 °C, α is the temperature coefficient of gas pressure equal to 1/273 deg -1. A graph of such a dependence on Рt-diagram has the form shown in Figure 1.7.

Rice. 1.7

2. Isobaric process. Gay-Lussac's law. R= const.

An isobaric process is a process that occurs at constant pressure P . 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: V/T= const.

Graph of an isobaric process on VT-the diagram is called isobar . It is useful to know the graphs of the isobaric process on PV- And RT-diagrams (Fig. 1.8).

Rice. 1.8

Isobar equation:

Where α =1/273 deg -1 - temperature coefficient of volumetric expansion. A graph of such a dependence on Vt diagram has the form shown in Figure 1.9.

Rice. 1.9

3. Isothermal process. Boyle-Mariotte law. T= const.

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: PV= const.

Graph of an isothermal process on PV-the diagram is called isotherm . It is useful to know the graphs of an isothermal process on VT- And RT-diagrams (Fig. 1.10).

Rice. 1.10

Isotherm equation:

(1.4.5)

4. Adiabatic process(isentropic):

An adiabatic process is a thermodynamic process that occurs without heat exchange with the environment.

5. Polytropic process. A process in which the heat capacity of a gas remains constant. The polytropic process is a general case of all the processes listed above.

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

7. Dalton's law. The pressure of a mixture of ideal gases is equal to the sum of the partial pressures P of the gases included in it:

(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.

If in some process the mass and temperature of the gas do not change, then such a process is called isothermal.

Atm= const T = const P 1 V 1 = P 2 V 2 orPV = const.

Received PV= const the equation is called equation of the isothermal process.

This equation was obtained by the English physicist Robert Boyle in 1662 and the French physicist Edmond Mariotte in 1676.

Equation P 1 /R 2 = V 2 / V 1 called the Boyle-Marriott equation.

The state of the gas is characterized by three macroparameters:

P - pressure,

V - volume,

T - temperature.

When graphically depicting a process, you can specify only two parameters that change, so the same process can be represented in three coordinate planes: ( R –V), (V – T), (P – T).

The graph of an isothermal process is called an isotherm. An isotherm depicted in a rectangular coordinate system (P – V), along the ordinate axis of which the gas pressure is measured, and along the abscissa axis its volume, is a hyperbola (Fig. 3).

The isotherm depicted in a rectangular coordinate system (V – T) is a straight line parallel to the ordinate axis (Fig. 4).

The isotherm depicted in a rectangular coordinate system (P – T) is a straight line parallel to the ordinate axis (Fig. 5).

Graphs of an isothermal process are depicted as follows:

ISOCHORIC PROCESS

Isochoric process a process that occurs at constant volume is called (V = const) and provided m = const and M = const.

Under these conditions, from the equation of state of an ideal gas for two temperatures T 0 and T it follows:

P 0 V = mRT 0

RV= MRTor R/R 0 = T/T 0

For a gas of a given mass, the ratio of pressure to temperature is constant if the volume of the gas does not change. When P 1 / P 2 = T 1 / T 2 (this equation is called Charles’s law), it is applicable for an isochoric process : V = const.

This is the equation of an isochoric process.

If V is the volume of gas at absolute temperature T, V 0 is the volume of gas at temperature 0 0 C; coefficient a equal to 1/273 K -1, called the temperature coefficient of volumetric expansion of gases, then the equation for an isochoric process can be written as P = P 0 × a ×T.

The curve of an isochoric process is called an isochore.

Isochora, depicted P – V), along the ordinate axis of which the gas pressure is measured, and along the abscissa axis - its volume, is a straight line parallel to the ordinate axis (Fig. 6).

Isochora, depicted in a rectangular coordinate system (V – T), is a straight line parallel to the abscissa axis (Fig. 7).

Isochora, depicted in a rectangular coordinate system (P – T), along the ordinate axis of which the gas pressure is measured, and along the abscissa axis its absolute temperature, is a straight line passing through the origin of coordinates (Fig. 8).

The dependence of gas pressure on temperature was experimentally studied by a French physicist Jacques Charles in 1787

An isochoric process can be carried out, for example, by heating air at a constant volume.

Graphs of an isochoric process are depicted as follows: