The process takes place at constant pressure. Basic thermodynamic processes. Constant temperature process

Heat capacity

The molar heat capacity at constant pressure is denoted as . In an ideal gas it is related to the heat capacity at constant volume by Mayer's relation.

Molecular kinetic theory makes it possible to calculate approximate values ​​of the molar heat capacity for various gases through the value of the universal gas constant:

Heat capacities can also be determined based on Mayer's equation if the adiabatic exponent is known, which can be measured experimentally (for example, by measuring the speed of sound in a gas or using the Clément-Desormes method).

Entropy change

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Isoprocesses processes that occur with a constant value of one of the parameters are called: pressure ( p) , volume ( V), temperature ( T).

Isoprocesses in gases are thermodynamic processes during which the amount of matter and pressure, volume, temperature or entropy do not change. Thus, when isobaric process pressure does not change when isochoric- volume, at isothermal- temperature, at isentropic- entropy (for example, a reversible adiabatic process). And the lines that display the listed processes on a certain thermodynamic diagram are called, respectively, isobar, isochore, isotherm And adiabatic. All these isoprocesses are special cases of a polytropic process.

Isochoric process.

Isochoric(or isochoric) process is a change in the thermodynamic system with the condition of no change in volume ( V = const). Isochoroy called a line that displays an isochoric process on a graph. This process describes Charles's law.

Isothermal process.

Isothermal process is a change in a thermodynamic system with the condition of no change in temperature ( T = const). Isotherm called a line that displays an isothermal process on a graph. This process describes Boyle-Mariotte law.

Isoentropic process.

Isoentropic process is a change in the thermodynamic system with the condition of no change in entropy ( S = const). 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:

pV γ = const,

Where γ — adiabatic index, determined by the type of gas.

Gas is one of four states of aggregation in which a substance can exist.

The particles that make up the gas are very mobile. They move almost freely and chaotically, periodically colliding with each other like billiard balls. Such a collision is called elastic collision . During a collision, they dramatically change the nature of their movement.

Since in gaseous substances the distance between molecules, atoms and ions is much greater than their sizes, these particles interact very weakly with each other, and their potential interaction energy is very small compared to the kinetic energy.

The connections between molecules in a real gas are complex. Therefore, it is also quite difficult to describe the dependence of its temperature, pressure, volume on the properties of the molecules themselves, their quantity, and the speed of their movement. But the task is greatly simplified if, instead of real gas, we consider it mathematical model - ideal gas .

It is assumed that in the ideal gas model there are no attractive or repulsive forces between molecules. They all move independently of each other. And the laws of classical Newtonian mechanics can be applied to each of them. And they interact with each other only during elastic collisions. The time of the collision itself is very short compared to the time between collisions.

Classical ideal gas

Let's try to imagine the molecules of an ideal gas as small balls located in a huge cube at a great distance from each other. Because of this distance, they cannot interact with each other. Therefore, their potential energy is zero. But these balls move at great speed. This means they have kinetic energy. When they collide with each other and with the walls of the cube, they behave like balls, that is, they bounce elastically. At the same time, they change the direction of their movement, but do not change their speed. This is roughly what the motion of molecules in an ideal gas looks like.

1. The potential energy of interaction between molecules of an ideal gas is so small that it is neglected compared to kinetic energy.
2. Molecules in an ideal gas are also so small that they can be considered material points. And this means that they total volume is also negligible compared to the volume of the vessel in which the gas is located. And this volume is also neglected.
3. The average time between collisions of molecules is much greater than the time of their interaction during a collision. Therefore, the interaction time is also neglected.

Gas always takes the shape of the container in which it is located. Moving particles collide with each other and with the walls of the container. During an impact, each molecule exerts some force on the wall for a very short period of time. This is how it arises pressure . The total gas pressure is the sum of the pressures of all molecules.

Ideal gas equation of state

The state of an ideal gas is characterized by three parameters: pressure, volume And temperature. The relationship between them is described by the equation:

Where R - pressure,

V M - molar volume,

R - universal gas constant,

T - absolute temperature (degrees Kelvin).

Because V M = V / n , Where V - volume, n - the amount of substance, and n= m/M , That

Where m - gas mass, M - molar mass. This equation is called Mendeleev-Clayperon equation .

At constant mass the equation becomes:

This equation is called united gas law .

Using the Mendeleev-Cliperon law, one of the gas parameters can be determined if the other two are known.

Isoprocesses

Using the equation of the unified gas law, it is possible to study processes in which the mass of a gas and one of the most important parameters - pressure, temperature or volume - remain constant. In physics such processes are called isoprocesses .

From The unified gas law leads to other important gas laws: Boyle-Mariotte law, Gay-Lussac's law, Charles's law, or Gay-Lussac's second law.

Isothermal process

A process in which pressure or volume changes but temperature remains constant is called isothermal process .

In an isothermal process T = const, m = const .

The behavior of a gas in an isothermal process is described by Boyle-Mariotte law . This law was discovered experimentally English physicist Robert Boyle in 1662 and French physicist Edme Mariotte in 1679. Moreover, they did this independently of each other. The Boyle-Marriott law is formulated as follows: In an ideal gas at a constant temperature, the product of the gas pressure and its volume is also constant.

The Boyle-Marriott equation can be derived from the unified gas law. Substituting into the formula T = const , we get

p · V = const

That's what it is Boyle-Mariotte law . From the formula it is clear that the pressure of a gas at constant temperature is inversely proportional to its volume. The higher the pressure, the lower the volume, and vice versa.

How to explain this phenomenon? Why does the pressure of a gas decrease as the volume of a gas increases?

Since the temperature of the gas does not change, the frequency of collisions of molecules with the walls of the vessel does not change. If the volume increases, the concentration of molecules becomes less. Consequently, per unit area there will be fewer molecules that collide with the walls per unit time. The pressure drops. As the volume decreases, the number of collisions, on the contrary, increases. Accordingly, the pressure increases.

Graphically, an isothermal process is displayed on a curve plane, which is called isotherm . She has a shape hyperboles.

Each temperature value has its own isotherm. The higher the temperature, the higher the corresponding isotherm is located.

Isobaric process

The processes of changing the temperature and volume of a gas at constant pressure are called isobaric . For this process m = const, P = const.

The dependence of the volume of a gas on its temperature at constant pressure was also established experimentally French chemist and physicist Joseph Louis Gay-Lussac, who published it in 1802. That is why it is called Gay-Lussac's law : " Etc and constant pressure, the ratio of the volume of a constant mass of gas to its absolute temperature is a constant value."

At P = const the equation of the unified gas law turns into Gay-Lussac equation .

An example of an isobaric process is a gas located inside a cylinder in which a piston moves. As the temperature rises, the frequency of molecules hitting the walls increases. The pressure increases and the piston rises. As a result, the volume occupied by the gas in the cylinder increases.

Graphically, an isobaric process is represented by a straight line, which is called isobar .

How more pressure in a gas, the lower the corresponding isobar is located on the graph.

Isochoric process

Isochoric, or isochoric, is the process of changing the pressure and temperature of an ideal gas at constant volume.

For an isochoric process m = const, V = const.

It is very simple to imagine such a process. It occurs in a vessel of a fixed volume. For example, in a cylinder, the piston in which does not move, but is rigidly fixed.

The isochoric process is described Charles's law : « For a given mass of gas at constant volume, its pressure is proportional to temperature" The French inventor and scientist Jacques Alexandre César Charles established this relationship through experiments in 1787. In 1802, it was clarified by Gay-Lussac. Therefore this law is sometimes called Gay-Lussac's second law.

At V = const from the equation of the unified gas law we get the equation Charles's law or Gay-Lussac's second law .

At constant volume, the pressure of a gas increases if its temperature increases. .

On graphs, an isochoric process is represented by a line called isochore .

The larger the volume occupied by the gas, the lower the isochore corresponding to this volume is located.

In reality, no gas parameter can be maintained unchanged. This can only be done in laboratory conditions.

Of course, an ideal gas does not exist in nature. But in real rarefied gases at very low temperatures and pressures no higher than 200 atmospheres, the distance between the molecules is much greater than their sizes. Therefore, their properties approach those of an ideal gas.

An isobaric process (also called an isobaric process) is one of the thermodynamic processes that occurs at a constant pressure. The gas mass of the system also remains constant. A visual representation of a graph demonstrating an isobaric process is given by a thermodynamic diagram in the corresponding coordinate system.

Examples

Most simple example An isobaric process can be called heating a certain volume of water in an open vessel. Another example is the expansion of an ideal gas in a cylindrical volume where the piston has a free stroke. In each of these cases the pressure will be constant. It is equal to ordinary atmospheric pressure, which is quite obvious.

Reversibility

An isobaric process can be considered reversible if the pressure in the system coincides with the external pressure and is equal at all times of the process (that is, it is constant in value), and the temperature changes very slowly. Thus, thermodynamic equilibrium in the system is maintained at every moment of time. It is the combination of the above factors that gives us the opportunity to consider the isobaric process reversible.

To carry out an isobaric process in a system, heat must be either supplied or removed. In this case, heat must be spent on the work of expansion of an ideal gas and on changing its internal energy. The formula demonstrating the dependence of quantities on each other during an isobaric process is called Gay-Lussac's law. It shows that volume is proportional to temperature. Let's derive this formula based on superficial knowledge.

Derivation of Gay-Lussac's law (primary understanding)

A person with at least a little understanding of molecular physics knows that many problems involve certain parameters. Their names are gas pressure, gas volume and gas temperature. In certain cases, molecular and molar mass, amount of substance, universal gas constant and other indicators are used. And there is a certain connection here. Let's talk about the universal gas constant in more detail. In case anyone doesn't know how they got it.

Obtaining the universal gas constant

This constant (a constant number with a certain dimension) is also called Mendeleev's constant. It is also present in the Mendeleev-Clapeyron equation for an ideal gas. How did our famous physicist obtain this constant?

As we know, the ideal gas equation has the following form: PV/T (which is pronounced as: “the product of pressure and volume divided by temperature”). The so-called Avogadro's law applies to the universal gas constant. It says that if we take any gas, then the same number of moles at the same temperature and the same pressure will occupy the same volume.

In fact, this is a verbal formulation of the equation of state of an ideal gas, which was written down as a formula a little earlier. If we take normal conditions (and this is when the gas temperature is 273.15 Kelvin, the pressure is 1 atmosphere, respectively, 101325 Pascals, and the volume of a mole of gas is 22.4 liters) and substitute them into the equation, multiply everything and divide, we get , that the totality of such actions gives us a numerical indicator equal to 8.31. The dimension is given in Joules divided by the product of a mole times Kelvin (J/mol*K).

Mendeleev-Clapeyron equation

Let's take the equation of state of an ideal gas and rewrite it in a new form. The initial equation, recall, has the form PV/T=R. Now let’s multiply both parts by the temperature indicator. We get the formula PV(m)=RT. That is, the product of pressure and volume is equal to the product of the universal gas constant and temperature.

Now let's multiply both sides of the equation by one or another number of moles. Let's denote their number by a letter, say, X. Thus, we get the following formula: PV(m)X=XRT. But we know that the product of V with the index “m” gives us as a result simply the volume V, and the number of moles X is revealed in the form of division private mass by molar mass, that is, it has the form m/M.

Thus, the final formula will look like this: PV=MRT/m. This is the same Mendeleev-Clapeyron equation, which both physicists came to almost simultaneously. We can multiply the right-hand side of the equation (and at the same time divide) by Avogadro's number. Then we get: PV = XN(a)RT/N(a). But the product of the number of moles by Avogadro’s number, that is, XN(a), gives us nothing more than total number gas molecules, designated by the letter N.

At the same time, the quotient of the universal gas constant and Avogadro's number - R/N(a) will give the Boltzmann constant (denoted by k). As a result, we will get another formula, but in a slightly different form. Here it is: PV=NkT. You can expand this formula and get the following result: NkT/V=P.

Gas work in an isobaric process

As we found out earlier, an isobaric process is a thermodynamic process in which the pressure remains constant. And to find out how work will be determined during an isobaric process, we will have to turn to the first law of thermodynamics. The general formula is as follows: dQ = dU + dA, where dQ is the amount of heat, dU is the change in internal energy, and dA is the work done during the thermodynamic process.

Now let's look specifically at the isobaric process. Let's take into account the fact that the pressure remains constant. Now let's try to rewrite the first law of thermodynamics for an isobaric process: dQ = dU + pdV. To get a clear idea of ​​the process and work, you need to depict it in a coordinate system. Let's denote the abscissa axis p, the ordinate axis V. Let the volume increase. At two distinct points with a corresponding value of p (fixed, of course), we note the states representing V1 (initial volume) and V2 (final volume). In this case, the graph will be a straight line parallel to the x-axis.

Finding work in this case is easier than ever. This will simply be the area of ​​the figure, limited on both sides by projections onto the abscissa axis, and on the third side by a straight line connecting the points lying, respectively, at the beginning and end of the isobar line. Let's try to calculate the value of the work using the integral.

It will be calculated as follows: A = p (integral from V1 to V2) dV. Let's expand the integral. We find that the work will be equal to the product of pressure and the difference in volumes. That is, the formula will look like this: A = p (V2 - V1). If we expand on some quantities, we get another formula. It looks like this: A = xR (T2 - T2), where x is the amount of substance.

Universal gas constant and its meaning

We can say that the last expression will determine physical meaning R - universal gas constant. To make it clearer, let's look at specific numbers. Let's take one mole of any substance to check. At the same time, let the temperature difference be 1 Kelvin. In this case, it is easy to notice that the work of the gas will be equal to the universal gas constant (or vice versa).

Conclusion

This fact can be presented in a slightly different light by rephrasing the wording. For example, the universal gas constant will be numerically equal to the work done in the isobaric expansion of one mole of an ideal gas if it is heated by one Kelvin. Calculating work for other isoprocesses will be somewhat more difficult, but the main thing is to apply logic. Then everything will quickly fall into place, and deriving the formula will be easier than you think.