Inner energy molecular physics. Calculation of changes in internal energy

Definition

Internal Body Energy (Systems) Call energy that is associated with all types of movement and interaction of particles constituting the body (system), including the energy of the interaction and movement of complex particles.

From the above, it follows that the internal energy does not include the kinetic energy of the movement of the center of mass system and the potential energy of the system caused by the action of external forces. This is energy that depends only on the thermodynamic state of the system.

Internal energy is most often denoted by the letter U. At the same time, its infinitely small change will be denoted by DU. It is believed that DU is a positive value if the internal energy of the system is growing, respectively, the internal energy is negative if the internal energy decreases.

The internal energy of the body system is equal to the sum of the internal energies of each individual body plus the interaction energy between the bodies inside the system.

Internal energy - system status function. This means that the change in the internal energy of the system during the transition of the system from one state to another does not depend on the method of transition (the type of thermodynamic process during transition) of the system and equals the difference in the internal energies of the final and initial states:

For a circular process, a complete change in the internal energy of the system is zero:

For a system, which does not apply external forces and internal energy, internal energy - the total energy of the system.

Internal energy can only be determined with an accuracy of some permanent terms (U 0), which is not determined by the methods of thermodynamics. However, this fact is not essential, since when using thermodynamic analysis, they deal with changes in internal energy, and not absolute values. Often u_0 are considered to be zero. At the same time, its components that change in the proposed circumstances are considered as internal energy.

Internal energy is considered limited and its boundary (lower) corresponds to T \u003d 0K.

Internal energy of perfect gas

The internal energy of the ideal gas depends only on its absolute temperature (T) and is proportional to the mass:

where C V is the heat capacity in isochoretum; C V - the specific heat capacity of the gas in isochoretum; - Internal energy per unit mass of gas with absolute zero temperatures. Or:

i - the number of degrees of freedom of the molecule of the ideal gas, V is the number of gas moles, R \u003d 8.31 J / (mol K) is a universal gas constant.

The first top of thermodynamics

As you know, the first beginning of thermodynamics has several wording. One of the wording that K. Karateodori suggested that the existence of internal energy as a component of the total energy of the system. It is a function of the state, in simple systems dependent on volume (V), pressure (P), mass substances (Mi), which make up this system : . In the formulation, which the internal energy gave the Karateodori is not the characteristic function of its independent variables.

In the more familiar formulations of the first start of thermodynamics, for example, the wording of the Helmholtz, the internal energy of the system is entered as the physical characteristics of the system. In this case, the behavior of the system is determined by the law of conservation of energy. Helmholtz does not define internal energy as a function of specific system status parameters:

- Change in internal energy in the equilibrium process, q is the amount of heat that the system received in the process under consideration, A is the work that the system has committed.

Units of Internal Energy Units

The main unit of measurement of internal energy in the SI system is: [u] \u003d J

Examples of solving problems

Example

The task. Calculate which magnitude the internal energy of helium having a lot of 0.1 kg will change if its temperature increased by 20 ° C.

Decision. When solving the problem, we consider helium with a single oriental perfect gas, then you can apply the formula for calculations:

Since we have with a single-catalog gas, then, the molar mass () take from the Mendeleev table ( kg / mol). The mass of gas in the presented process does not change, therefore, the change in internal energy is:

All values \u200b\u200brequired for calculations are available:

Answer. (J)

Example

The task. The perfect gas was expanded in accordance with the law, which is depicted by the schedule in Fig. 1. from the initial volume v 0. When expanding the volume of Sal is equal. What is the increment of the internal energy of gas in a given process? The adiabatic coefficient is equal.

To solve the practical issues, the internal energy itself plays a significant role, but its change Δ U. = U. 2 - U. one . The change in the internal energy is calculated based on the laws of energy conservation.

The internal energy of the body may vary in two ways:

1. When committing mechanical work.

a) If the external force causes deformation of the body, then the distances between the particles are changed from which it consists, and therefore, the potential energy of the interaction of particles changes. With inelastic deformations, in addition, the body temperature changes, i.e. The kinetic energy of the thermal motion of particles changes. But when the body is deformed, work is performed, which is a measure of changing the inner energy of the body.

b) the internal energy of the body varies also with its inelastic collision with another body. As we have seen before, with an inelastic collision, their kinetic energy decreases, it turns into an inner (for example, if you hit the hammer on the wire lying on the anvil several times, the wire is warm). The measure of changing the kinetic energy of the body is, according to the theorem on kinetic energy, the work of the current forces. This work can serve as a measure of changes in internal energy.

c) Changing the internal energy of the body occurs under the action of friction force, since, as is known from experience, friction is always accompanied by a change in the temperature of the rubbing tel. The work of friction force can serve as a measure of changes in internal energy.

2. Using heat exchange. For example, if the body is placed in the flame burner, its temperature will change, therefore, its internal energy will change. However, no work was done here, for it did not occur to the visible movement of the body itself or its parts.

Changing the internal energy of the system without performing the work is called heat exchange (heat transfer).

There are three types of heat exchange: thermal conductivity, convection and radiation.

but) Thermal conductivity The heat exchange process between the bodies (or parts of the body) is called direct contact due to the thermal chaotic movement of body particles. The amplitude of oscillations of solid body molecules is greater than above its temperature. The thermal conductivity of gases is due to the exchange of energy between gas molecules during their collisions. In the case of liquids, both mechanisms work. The thermal conductivity of the substance is maximum in solid and minimal in a gaseous state.

b) Convection It is a heat transfer of heated fluid flows or gas from some sections of them by volume to others.

c) heat exchange when radiation It is carried out at a distance through electromagnetic waves.

Consider in more detail how to change internal energy.

Quantity of heat

As is known, a change in mechanical energy occurs at various mechanical processes. W.. The measure of changes in mechanical energy is the work of the forces attached to the system:

With heat exchange, a change in the internal energy of the body occurs. The measure of changes in the internal energy under heat exchange is the amount of heat.

Quantity of heat - This is a measure of changes in internal energy in the heat exchange process.

Thus, work, and the amount of heat characterize the change in energy, but not identical internal energy. They do not characterize the state of the system (as internal energy does), but determine the energy transition process from one species to another (from one body to another) when the state changes significantly depend on the nature of the process.

The main difference between the work and the amount of warmth is that

§ work characterizes the process of changing the internal energy of the system, accompanied by the conversion of energy from one species to another (from mechanical internal);

§ The amount of heat characterizes the process of transmitting internal energy from some bodies to another (from more heated to less heated), not accompanied by energy transformations.

§ Heat capacity, The amount of heat spent to change the temperature by 1 ° C. According to a more stringent definition, heat capacity - Thermodynamic value determined by the expression:

§ where Δ. Q. - The amount of heat reported by the system and caused the change in its temperature to DELTA; T. The ratio of finite differences Δ Q./ ΔT is called average heat Cool, the attitude of infinitely small values \u200b\u200bD Q / dt. - True heat Cool. Since D. Q. is not a complete differential function of the status function, then heat capacity Depends on the path of transition between the two states of the system. Distinguish heat capacity Systems in general (J / K), specific heat capacity [J / (r · k)], molar heat capacity [J / (mol · k)]. In all below the formulas, molar values \u200b\u200bare used heat capacity.

Question 32:

Internal energy can be changed in two ways.

The amount of heat (Q) is called the change in the internal energy of the body, which is due to heat transfer.

The amount of heat is measured in the SI system in Joules.
[Q] \u003d 1J.

The specific heat capacity of the substance shows how much heat is needed to change the temperature of the mass of this substance by 1 ° C.
Unit of specific heat in the SI system:
[C] \u003d 1J / kg · Gradus.

Question 33:

33 The first top of the thermodynamics the amount of heat obtained by the system goes to change its internal energy and performing work on external bodies. DQ \u003d DU + DA, where DQ-elementary amount of heat, DA-elementary work, DU-increment of internal energy. The use of the first start of thermodynamics to isoprocesses
Among the equilibrium processes occurring with thermodynamic systems, stand out isoprocesseesunder which one of the main parameters of the state is stored constant.
Isochhore process (V.\u003d const). Diagram of this process (isoker)in coordinates r, V. are depicted direct, parallel axis of the ordinate (Fig. 81), where the process 1-2 There are isoormal heating, and 1 -3 - Isoormal cooling. With a hegoic process, the gas does not make work on external bodies, Isothermal process (T.\u003d const). As already mentioned § 41, the isothermal process is described by the law of Boyle Mariotta
In order to increase the temperature when the gas expansion is expanded, the amount of heat equivalent to the external work of the expansion is required during the isothermal process.

Question 34:

34 Adiabatic is called a process in which there is no heat exchange ( dQ \u003d.0) between the system and the environment. Adiabatic processes include all the speed-tracting processes. For example, the adiabatic process can be considered the process of propagation of sound in the medium, since the speed of propagation of the sound wave is so large that the exchange of energy between the wave and the medium does not have time to happen. Adiabatic processes are used in internal combustion engines (expansion and compression of the combustible mixture in the cylinders), in refrigeration plants, etc.
From the first beginning of the thermodynamics ( dQ \u003d.d. U + DA) for the adiabatic process it follows that
p / s v \u003d γ, we will find

Integrating the equation ranging from P 1 to P 2 and, accordingly, from V 1 to V 2, and potentiation, we will come to expression

Since states 1 and 2 are selected arbitrarily, then you can record

Thermodynamics as a discipline was formed by the middle of the 19th century. This happened after the discovery of the Law on the Conservation of Energy. There is a certain relationship between thermodynamics and molecular kinetics. What place in theory is internal energy? Consider this in the article.

Statistical mechanics and thermodynamics

The initial scientific theory of thermal processes was not molecular kinetic. The first was thermodynamics. It was formed in the process of studying the optimal conditions for the use of heat for work. It happened in the middle of the 19th century, before the molecular kinetics received recognition. To date, both thermodynamics and molecular-kinetic theory are used in technology and science. The latter in theoretical physics is referred to as statistical mechanics. It, along with thermodynamics, examines the same phenomena using various methods. These two theories mutually complement each other. The basis of thermodynamics is compiled by two laws. Both of them relate to energy behavior and are established by experience. These laws are valid for any substance, regardless of the internal structure. Statistical mechanics are considered to be deeper and accurate science. Compared to thermodynamics, it represents greater difficulty. It is used in the case when thermodynamic ratios are insufficient to explain the studied phenomena.

Molecular kinetic theory

By the middle of the 19th century, it was proved that along with the mechanical exists internal energy of macroscopic bodies. It enters the balance of energy natural transformations. After the internal energy was opened, the position was formulated about its preservation and transformation. While the washer, moving on ice, stops under the influence of friction force, its kinetic (mechanical) energy does not just cease to exist, but also passes the molecules of washers and ice. When the irregularities of the surfaces of bodies undergoing friction are deformed. In this case, the intensity of moving random molecules increases. When heated both tel, internal energy increases. It is not difficult to observe the reverse transition. When the water is heated in a closed tube, the internal energy (and its, and the resulting steam) begins to increase. Pressure will increase, with the result that the plug will be supplanted. The internal energy of the pair will cause an increase in kinetic energy. In the process of expanding couples makes work. In this case, its internal energy decreases. As a result, steam cooling occurs.

Internal energy. general information

With the random movement of all molecules, the sum of their kinetic energies, as well as the potential energies of their interactions, is internal energy. Considering the position of molecules relative to each other and their movement, it is almost impossible to calculate this amount. This is due to a huge number of elements in macroscopic bodies. In this regard, you must be able to calculate the value in accordance with the macroscopic parameters that can be measured.

Singo-name gas

The substance is considered rather simple in its properties, since it consists of individual atoms, and not molecules. The monatomic gases include argon, helium, neon. The potential energy in this case is zero. This is due to the fact that molecules in perfect gas do not interact with each other. The kinetic energy of a messy molecular movement is determined for internal (U). In order to calculate the single-name gas weighing M, we need to multiply the kinetic energy (medium) of the 1st atom for the total number of all atoms. But it should be borne in mind that KNA \u003d R. Based on the data we have, we get the following formula: U \u003d 2/3 x M / M x RT,where the internal energy is directly proportional to the absolute temperature. All changes u are defined only t (temperature) measured in the initial and final state of the gas, and do not have a direct relationship to volume. This is due to the fact that the interactions of its potential energy are equal to 0, and they are not at all dependent on other system parameters of macroscopic objects. With more complex molecules, the perfect gas will also have internal energy, directly proportional to the absolute temperature. But, I must say, at the same time, between u and t, the ratio of proportionality will change. After all, complex molecules perform not only progressive movements, but also rotational. Internal energy is equal to the sum of these movements of molecules.

What does u depend?

Internal energy is influenced by one of the macroscopic parameters. This temperature. In real gases, liquid and solid bodies, the potential energy (average) during the interaction of molecules is not equal to zero. Although, if you consider more accurate, it is much less kinetic for gases (middle). At the same time, for solid and liquid bodies, it is comparable to it. But the average U depends on V substance, because during its change, the average distance is also changing, which is between molecules. From this it follows that in thermodynamics the internal energy depends not only on temperature T, but also from V (volume). Their value uniquely determines the state of bodies, and therefore u.

World Ocean

It is difficult to submit what incredibly large energy reserves contains the world ocean. Consider what the inner energy of water represents. It should be noted that it is thermal, because it was formed as a result of overheating with a liquid part of the ocean surface. So, having a difference, for example, in 20 degrees in relation to bottom water, it acquires a value of about 10 ^ 26 J. When measuring flows in the ocean, its kinetic energy is estimated by a value of about 10 ^ 18 J.

Global problems

There are global problems that can be placed on the global level. These include:

Depletion of fossil fuel reserves (primarily oil and gas);

Significant environmental pollution associated with the use of these fossils;

Thermal "pollution", plus the increase in the concentration of atmospheric carbon dioxide, threatening with global climatic disorders;

The use of uranium reserves leading to the emergence of radioactive waste, which very negatively affect the vital activity of all living things;

Use of thermonuclear energy.

Conclusion

All this uncertainty regarding the expectations of the consequences that will certainly come, if not cease to consume energy, produced in such ways, forces scientists and engineers to pay almost all their attention to solving this problem. Their main task is to search for an optimal energy source, it is also important and the involvement of various natural processes. Among them are the greatest interest: the sun, or rather sunny heat, wind and energy in the ocean.

In many countries of the sea and the oceans have long been viewed as a source of energy, and their prospects are becoming increasingly promising. The ocean is in itself a lot of secrets, its inner energy is a bottomless storage facilities. It is only one of how many ways to extract energy it provides us (such as ocean flows, the energy of tides and tide, thermal energy and others), already makes thinking about his greatness.

Energy is a common measure of various forms of motion of matter. Accordingly, the forms of motion of matter distinguish between the types of energy - mechanical, electrical, chemical, etc. Any thermodynamic system in any condition has some reserve of energy, the existence of which was proven by R. Clausius (1850) and received the name of internal energy.

Internal energy (U) is the energy of all types of movement of microparticles that make up the system, and the energy of their interaction among themselves.

The internal energy is consisted of the energy of the translational, rotational and oscillatory movement of particles, the energy of intermolecular and intramolecular, intra-industrial and intracererial interactions, etc.

Energy of intramolecular interaction, i.e. The energy of the interaction of atoms in the molecule is often called chemical energy . Changing this energy takes place in chemical transformations.

For thermodynamic analysis, there is no need to know from which forms of motion of the matter there is an internal energy.

The supply of internal energy depends only on the state of the system. Consequently, the internal energy can be considered as one of their characteristics of this state on a par with such values \u200b\u200bas, pressure, temperature.

Each state of the system corresponds to a strictly defined value of each of its properties.

If the homogeneous system in the initial state has volume V 1, pressure P 1, temperature T 1, internal energy U 1, specific electrical conductivity æ 1, etc., and in the finite state, these properties are respectively equal to V 2, P 2, T 2, U 2, æ 2, etc., the change in each property when switching the system from the initial state to the final will be the same, regardless of how the system is moving from one state to another: the first, second or third (rice . 1.4).

Fig. 1.4 Independence of the properties of the system from the path of its transition

from the usual state to another

Those. (U 2 - u 1) i \u003d (u 2 - u 1) ii \u003d (u 2 - u 1) iii (1.4)

Where are the figures I, II, III, etc. Indicate the paths of the process. Therefore, if the system from the initial state (1) in the final (2) will switch to one path, and from the final at the beginning - on the other path, i.e. A circular process (cycle) is performed, the change in each properties of the system will be zero.

Thus, the change in the status function of the system does not depend on the path of the process, and depends only on the initial and end states of the system. The infinitely small change in the properties of the system is usually the differential sign D. For example, Du is an infinite small change in internal energy, etc.

Energy exchange form

In accordance with various forms of motion of matter and various types of energy, there are various forms of energy exchange (energy transmission) - forms of interaction. Thermodynamic examines two forms of energy exchange between the system and the environment. This is work and heat.

Work.The most visual form of energy exchange is a mechanical work corresponding to the mechanical form of motion of matter. It is produced when the body is moved under the action of mechanical strength. In accordance with other forms of movement of matter, other types of work are distinguished: electrical, chemical, etc. The work is a form of transmission of an ordered, organized movement, since when performing the body, the body particles move organized in one direction. For example, performing work when expanding gas. Gas molecules in the cylinder under the piston are in chaotic, disordered movement. When the gas begins to move the piston, that is, to make a mechanical work, an organized movement will be imposed on the erratic movement of gas molecules: all molecules receive some displacement in the direction of the movement of the piston. Electric work is also associated with the organized movement in a certain direction of charged particles of matter.

Since work is a measure of transmitted energy, its amount is measured in the same units as energy.

Heat. The shape of the energy exchange corresponding to the chaotic movement of microparticles constituting the system is called heat exchange, and the amount of energy transmitted under heat exchange is called heat.

The heat exchange is not associated with a change in the position of the bodies constituting the thermodynamic system, and consists in direct energy transmission by molecules of one body by the molecules of the other during their contact.

P redust the insulated vessel (system) separated into two parts with a heat-conducting partition AV (Fig. 1.5). Suppose that in both parts of the vessel is gas.

Fig. 1.5. To the concept of warmth

In the left half of the vessel, the temperature of the gas T 1, and in the right 2. If t 1\u003e t 2, then the average kinetic energy ( ) Gas molecules on the left side of the vessel, there will be more middle kinetic energy ( ) In the right half of the vessel.

As a result of continuous collisions of molecules about the partition in the left half of the vessel, the partition molecules are transmitted. The molecules of gas located in the right half of the vessel, facing the partition, will acquire some part of the energy from its molecules.

As a result of these clashes, the kinetic energy of molecules in the left half of the vessel will decrease, and in the right - increase; Temperatures T 1 and T 2 will be aligned.

Since the heat is a metering energy, its number is measured in the same units that energy. Thus, heat exchange and work are forms of energy exchange, and the amount of heat and the amount of operation are measures of the transmitted energy. The difference between them is that the heat is a form of transmission of the microphysical, disordered movement of particles (and, accordingly, the energy of this movement), and the work is the form of energy transfer of an ordered, organized motion of matter.

Sometimes they say: the heat (or work) is supplied or removed from the system, and it should be understood that it should be supplied and the heat and work is given, and energy, therefore, it is not necessary to use this kind of expressions as the "heat supply" or "heat contain".

As the shape of the energy exchange (forms of interaction) of the system with the environment, heat and work cannot be associated with any specific state of the system, they cannot be its properties, and, therefore, the functions of its condition. This means that if the system passes from the initial state (1) to the final (2) various paths, the heat and work will have different values \u200b\u200bfor different transition paths (Fig. 1.6)

The final amount of heat and work is denoted by Q and A, and infinitely small values \u200b\u200baccording to ΔQ and Δa. The values \u200b\u200bof ΔQ and Δa, in contrast to DU, are not a complete differential, because Q and A are not status functions.

When the process of the process is predetermined, work and heat will acquire properties of the system status functions, i.e. Their numerical values \u200b\u200bwill be determined only by the initial and end states of the system.

Along with mechanical energy, any body (or system) has internal energy. Internal energy - rest energy. It consists of thermal chaotic movement of molecules that make up the body, the potential energy of their relative position, the kinetic and potential energy of electrons in atoms, nucleons in the nuclei and so on.

In thermodynamics it is important to know the absolute value of the internal energy, but its change.

In thermodynamic processes, only the kinetic energy of moving molecules (thermal energy is not enough to change the structure of the atom, and even more so the kernel) is changed. Consequently, actual under internal energy In thermodynamics implies energy heat chaotic Movement molecules.

Internal energy U. One mole of perfect gas is equal to:

In this way, internal energy depends only on temperature. Internal energy U is a system status function, Regardless of the background.

It is clear that in the general case the thermodynamic system can possess both internal and mechanical energy, and different systems can exchange these types of energy.

Exchange mechanical energy Characterized perfect work a, And the exchange of internal energy - the amount of transmitted heat Q.

For example, in the winter you threw a hot stone in the snow. Due to the reserve of potential energy, mechanical work was performed on ground crumpled, and due to the internal energy stock, the snow was melted. If the stone was cold, i.e. The temperature of the stone is equal to the temperature of the medium, then only work will be performed, but there will be no exchange of internal energy.

So, work and heat do not eat special forms of energy. It is impossible to talk about the reserve of warmth or work. it measure transmitted Another system of mechanical or internal energy. Here is the reserve of these energies you can talk. In addition, mechanical energy can go to thermal energy and back. For example, if you knock the hammer on the anvil, then after a while the hammer and anvil are warm up (this is an example dissipation Energy).

You can learn more of the mass of the conversion of one form of energy to another.

Experience shows that in all cases the transformation of mechanical energy into thermal and is always performed in strictly equivalent quantities. This is the essence of the first start of thermodynamics, following the law of energy conservation.

The amount of heat reported by the body goes to an increase in internal energy and to the body of work:

- That's what it is the first top of thermodynamics , or the law of conservation of energy in thermodynamics.

Rule of signs: If the heat is transmitted from the environment this system, And if the system works on the surrounding bodies, while. Given the rule of signs, the first top of the thermodynamics can be written as:

In this expression U. - system status function; D. U. - its full differential, and δ Q. and Δ. BUT These are not. In each state, the system has defined and only with such a value of internal energy, so you can write:

,

It is important to note that heat Q. and work BUT depend on how the transition from state 1 to state 2 (isoochetically, adiabatically, etc.), and internal energy U. does not depend. At the same time, it is impossible to say that the system has the meaning and work determined for this state.

From formula (4.1.2) it follows that the amount of heat is expressed in the same units that work and energy, i.e. in Joules (J).

Of particular importance in thermodynamics have circular or cyclic processes in which the system, passing a series of states, returns to the original one. Figure 4.1 shows the cyclic process 1- but–2–b.-1, while the work of A.

Fig. 4.1.

As U. - status function, then

This is true for any status function.

If then according to the first beginning of the thermodynamics, i.e. It is impossible to build a periodically operating engine that would have done more than work than the amount of energy reported to him. In other words, the perpetual motion of the first kind is impossible. This is one of the formulations of the first start of thermodynamics.

It should be noted that the first beginning of thermodynamics does not indicate, in which direction processes of changes in the state, which is one of its flaws.