A change in the state of a system, characterized by a change in its thermodynamic parameters, is called thermodynamic process . In other words, if the system passes from the initial state to the final state, which is different from the initial one, then a process is performed. The following processes are most often considered in thermodynamics:

1) isothermal (T = const), (Greek therme - heat, warmth);

2) isobaric(R = const), (Greek baros - heaviness, weight);

3) isochoric ((V = const), (Greek chora - space);

4) isobaric-isothermal(R = const, T= const);

5) isochoric-isothermal(V = const, T= const);

6) adiabatic(there is no exchange of heat between the system and the external environment).

The process, as a result of which the system, having left the initial state and undergoing a series of transformations, returns to it again, is called circular process or cycle.

A change in the state of the system can occur under various conditions. Therefore, first of all, they distinguish equilibrium (quasi-static) and nonequilibrium processes. A process considered as a continuous series of equilibrium states of a system. called equilibrium process . In an equilibrium process, all the parameters of the system change infinitely slowly, so that the system is always in a state of equilibrium.

For a thermodynamic process to be carried out quasi-statically (in equilibrium), the following conditions must be met:

1. An infinitely small difference between acting and opposing forces (for example, the pressure in the system differs by an infinitesimal amount from the external pressure).

2. Infinitely slow process.

3. Making the maximum work (in a non-equilibrium process, the work is always less than in an equilibrium one and can be equal to zero - for example, the expansion of an ideal gas into a vacuum).

4. Changing the external force by an infinitesimal value reverses the direction of the process.

5. The absolute values ​​of the work of the direct and reverse processes are the same, and their paths are the same.

The process of transition of a system from a non-equilibrium state to an equilibrium state is called relaxation , and the duration of this process is time relaxation . Different processes have different relaxation times: from 10 -7 seconds to establish an equilibrium pressure in the gas to several years when equalizing the concentrations in hard alloys.

It should be noted that real processes occur when the balance between the system and the environment is disturbed, and energy and or substance flows arise inside the system, breaking the balance in it. Therefore, real processes that occur with a violation of the equilibrium state of the system are nonequilibrium . In classical (phenomenological) thermodynamics, only equilibrium processes are studied. The conclusions obtained by thermodynamics for equilibrium processes play the role of a kind of limit theorems in it.

Physically infinitely slow or quasi-static (equilibrium) change any parameter " a” is called such a change over time, when the rate of change da/dt much less than the average rate of change of this parameter during relaxation (here t- time). If during relaxation the parameter « a» changed to Δ a, and the relaxation time τ , then at equilibrium processes

If changing the parameter " a» happens in time t, less than or equal to the relaxation time τ , so

then such a process is nonequilibrium or non-static .

In addition to the concepts of equilibrium (quasi-static) and non-equilibrium processes in thermodynamics, all processes are divided into reversible and irreversible . Reversible thermodynamic process - the process of transition of a thermodynamic system from one state to another, which can proceed both in the forward and in the opposite direction through the same intermediate states without any changes in the environment. If the process of transition of the system from one state to another cannot be carried out in the forward and reverse directions without changes in the environment, then it is called irreversible process. It's obvious that an equilibrium process is always reversible, and a reversible process always proceeds in an equilibrium way.

Examples of irreversible processes:

1. The heat transfer process at a finite temperature difference is irreversible. A reversible process (as an equilibrium process) begins with a state of equilibrium. The presence of a temperature difference indicates the non-equilibrium (non-static) process.

2. Expansion of gas into vacuum is irreversible, since with such an expansion no work is done, and it is impossible to compress the gas so as not to do work.

3. The process of diffusion of gases is irreversible. If in a vessel with two different gases separated by a partition, the partition is removed, then each gas will diffuse into the other. To separate gases, each of them must be compressed. In order for them not to heat up, it is necessary to take away heat from them and turn them into work, which is impossible without a change in the environment (the second law of thermodynamics).

Thermodynamic processes. 2.3.1. The concept of a thermodynamic process

2.3.1. The concept of a thermodynamic process

A general idea of ​​the state of the system and its changes (processes) is set out in subclause 1.1.3.

A thermodynamic process is a certain sequence of changing the parameters of the state of the working fluid of the system.

Thermodynamic processes can be equilibrium and non-equilibrium, reversible and irreversible. If a change in the state of a thermodynamic system proceeds with a violation of its internal equilibrium, then a nonequilibrium thermodynamic process takes place. Real processes observed in nature, in experiment, in machines, are non-equilibrium, their description by thermodynamic methods is impossible.

In order to study the basic properties of systems in the exchange of energy with the environment, the approach of scientific abstraction is used, real processes are idealized, taking them for equilibrium.

A thermodynamic process proceeding with an infinitesimal

deviation of the state of the system from equilibrium is called

r a v n o v e s n y m.

The concept of reversible and irreversible processes is described in subparagraph 1.1.5. Below we consider only equilibrium and reversible thermodynamic processes of an ideal perfect gas.

For an equilibrium thermodynamic system, the relationship between thermodynamic parameters is established by the equation of state for an ideal gas (2.9). Consequently, this equation is also valid for an equilibrium thermodynamic process not only in the initial and final states of the system, but also in any of its intermediate states.

In the general case, two of the three thermodynamic parameters can change arbitrarily (independently) in the process. The study of the operation of heat engines shows that specific thermodynamic processes are of greatest interest for practice, namely, changes in state occurring at constant pressure, volume, and temperature, and also without heat exchange with the environment. Their characteristic feature is that for a perfect gas, the heat capacity remains unchanged throughout the process.

In thermodynamics, graphical methods for analyzing processes are widely used. In this case, it is more convenient to use non-spatial three-dimensional images of lines described by the function f(p, v, T), and their two-dimensional projections onto one of the three coordinate planes. As a rule, a graphical representation of thermodynamic processes is used in coordinates pv and Ts, and in special cases - in coordinates i s; pi; id etc.

In pv and Ts - coordinates in Fig.2.3 and 2.4 shows an arbitrary

thermodynamic process of changing parameters from state 1 to state 2.

Fig 2.3 Fig. 2.4

On fig. 2.3 area bounded by process curve 1-2, abscissa and extreme ordinates a and b, as shown in 1.2.5, is numerically equal to the work of expansion, and the area bounded by the process curve, the ordinate axis and the extreme abscissas c and d, technical work.

AT Ts- coordinates the area bounded by the process curve 1-2, the abscissa axis and extreme ordinates a and b, is expressed by the integral:

F a-1-2-b =

Because the dq = Tds or q =, then F a-1-2-b is numerically equal to the heat supplied in the process.

Since these areas depend on the nature of the process, heat and work are its functions.

Regardless of the features, the process of their analysis is carried out in a certain sequence, which is as follows:

- the nature of the process is established, a constant parameter is assigned;

- using the first law of thermodynamics and specific features of the process, its equation is derived;

A thermodynamic process is understood as a set of successive states through which a thermodynamic system passes when it interacts with the environment.

The state of a thermodynamic system can be equilibrium and non-equilibrium. equilibrium such a state of the system is called in which at all points of its volume all state parameters and physical properties are the same (pressure, temperature, specific volume, etc.). In thermodynamics, it is postulated that an isolated system always comes to a state of thermodynamic equilibrium over time and can never spontaneously leave it.

All processes occurring in a thermodynamic system are divided into equilibrium and non-equilibrium. equilibrium such processes are called when the system goes through a series of successive equilibrium states. If the process proceeds so slowly that equilibrium is established at each moment of time, then such processes are called quasi-static. These processes have properties of reversibility.

non-equilibrium processes are called such processes during which the system is not in a state of equilibrium. The process of transition of a system from a non-equilibrium state to an equilibrium state is called relaxation and the transition time to equilibrium is relaxation time.

All real processes occurring in nature are non-equilibrium. This is determined by the fact that when the process proceeds at a finite speed, an equilibrium state does not have time to establish in the working body. For example, during the rapid expansion of gas in a cylinder with a piston, the temperature and pressure at different points of the volume of the working fluid will not be the same, t.s. a non-equilibrium state will take place, and the process itself will be non-equilibrium. Consequently, real processes, being non-equilibrium, can only approach equilibrium to some extent, never exactly coinciding with them.

However, thermodynamics primarily considers equilibrium processes and equilibrium states, since only equilibrium states can be described quantitatively using equations of state. Only equilibrium processes of changing the state of a thermodynamic system can be represented graphically. Any arbitrarily taken equilibrium state in a triaxial coordinate system pvt is represented by a point, and the set of these points with a continuous change in state is a certain curve, which is a graphic representation of an equilibrium process. However, it is difficult to use a triaxial coordinate system, therefore, in practice, projections of the curves of a triaxial system on a plane in a rectangular coordinate system are used. In technical thermodynamics, a biaxial coordinate system is most often used to study equilibrium thermodynamic processes pv. In this coordinate system, the vertical represents isochoric process, horizontal - isobaric, hyperbolic curve - isothermal(Fig. 1.2). Besides,

Rice. 1.2.

processes are considered in thermodynamics adiabatic, which takes place in the absence of heat transfer (dq= 0) and polytropic(generalizing process), special cases of which are the first four processes.

Any state parameter is also a state function, since its change in any thermodynamic process does not depend on the type of process, but is determined only by the initial and final states.

Thermodynamic processes also include circular process, or cycle. A cycle is a set of processes that return the system to its original state. In the diagrams, the cycle is depicted as a closed contour, the form of which is completely determined by the number and shape of the processes that make up the cycle. The graphic representation and study of cycles in a spatial coordinate system would be even more difficult than the representation of individual processes. Therefore, the cycle is also projected onto one of the coordinate planes.

Thermodynamic processes.

Any thermodynamic process can occur only if the mechanical or thermal equilibrium is disturbed, i.e. when the gas is compressed or expanded (the pressure of the medium is greater or less than the pressure of the gas), when the gas is heated or cooled (the temperature of the medium is greater or less than the temperature of the gas). The more the equilibrium is disturbed, the faster the process in the general case takes place and the more sharply the state of rest of the gas will be disturbed.

During the thermodynamic process, the equilibrium parameters of the system (body) will change, the relationship between which is given by the equation of state f(p,V,T)=0, and internal energy, the change of which can be determined by an equation of the form f(U, T, V)=0.

In thermodynamics, processes subject to regularities expressed by the condition φ=const are called polytropic(with Greek manifold). The change in gas parameters in a polytropic process is determined by the value n, called the indicator polytropes and for each process it is constant.

Study of processes at different values n leads us to some special cases of polytropic processes, which are especially distinguished in the study:

Isobaric process (constant pressure), polytropic index is 0;

Isothermal process (constant temperature), polytropic index is 1;

An adiabatic process (a process without heat exchange with the surrounding space), the polytropic index is equal to a constant number;

Isochoric process (the volume is constant), the polytropic exponent is equal to the set.

The property of a substance that indicates the amount of energy that can be converted into heat is called - enthalpy. This means that while matter can have energy based on temperature and pressure, not all of it can be converted to heat. Part of internal energy always remains in matter and maintains its molecular structure. Part of the kinetic energy of a substance is not available when its temperature approaches the ambient temperature. enthalpy defined as the total energy of matter, since it is equal to the sum of its internal energy (u) in a given state along with its ability to convert heat into work at a certain temperature and pressure (pv). But in reality, enthalpy does not indicate the total energy of a substance at a given temperature above absolute zero (-273°C). Therefore, instead of defining enthalpy as the total heat of a substance, more precisely define it as the total amount of available energy of a substance that can be converted into heat.

H=U+pV

Enthalpy units- British thermal unit or joule for energy and Btu/lbm or J/kg for specific energy.

Consider what is the efficiency of a heat engine

Thermal efficiency

If there are different cyclic heat engines operating between temperatures T 1 and T 2 and if some of these systems are reversible, then the efficiency all systems is the same, and irreversible ones will have an efficiency. not exceeding efficiency reversible systems.

Nothing but the force of friction prevents us from bringing the efficiency of a simple mechanism (lever, block, gate, etc.) up to 100%. All the mechanical energy of the body can be converted into internal, into the internal energy of the body itself and the surrounding bodies.

J/°C

This quantity is called entrapy.

The first law of thermodynamics establishes the existence in any equilibrium system of a single-valued state function - internal energy, which does not change in the absence of external influences during any processes within the system.

The second law of thermodynamics establishes the existence in any equilibrium system of another unambiguous state function - entropy, which, however, unlike internal energy, does not change in an isolated system only in equilibrium processes and always increases in non-equilibrium processes in it. Thus, The second law of thermodynamics is the law of entropy.

You can combine the mathematical expressions of the first and second laws of thermodynamics in one equation:

first

second

where we get

This relation, covering the first and second laws of thermodynamics, is called the thermodynamic identity. All derived equations are applicable for reversible cycles and processes.

Without external influence, processes can proceed only if the entropy is constant (for reversible processes) or increases (irreversible processes).

It is impossible to build a machine that could turn it into work due to the heat from cooled bodies.

The maximum value of the entropy of a closed system is reached when the system comes to a state of thermodynamic equilibrium. Such a quantitative formulation of the second law of thermodynamics was given by Clausius.

The transition from a non-equilibrium state to an equilibrium state is a transition from a state that can be carried out in a smaller number of ways to a state that can be carried out in a much larger number of ways. The most probable for a closed system will be the state that is realized in the greatest number of ways, i.e. state of thermal equilibrium.

At the same time, the spontaneous exit of the system from the state of equilibrium would be unlikely. The number of ways in which a given equilibrium state can be realized is called the thermodynamic probability ω.

The number of ways ω in which a given state of a system, consisting, for example, of two bodies, can be realized, is equal to the product of the numbers of ways ω 1 and ω 2, in which the states of each of these bodies separately can be realized

ω syst = ω 1 ω 2

The thermodynamic probability is not related to the thermal characteristics of the system, but only to the mechanical ones.

In this case, the entropy will be equal to

where K is the universal gas constant, referred to one molecule and is equal to 1.38∙10 -23 J/°С

K=R/N A

where R is the gas constant;

N A is the number of the avant-garde.

The entropy of a chemically homogeneous body of finite density, as the temperature tends to absolute zero, tends to a limiting value that does not depend on pressure, density, or phase. It is therefore convenient to take the state at 0°K as some initial state and to assume that

This equation is called Nerst's law or the third law of thermodynamics.

Then the entropy of an arbitrary state is determined uniquely. The entropy found in this way is sometimes called the absolute entropy.

The thermodynamic state of the system at absolute zero corresponds to only one thermodynamic state with the lowest energy compatible with a given crystal structure or with a given state of aggregation of the system.

Lecture 2

MPC for NPP emissions 0.05 Sv/year for personnel 0.005 Sv/year for population nearby

A thermodynamic system can only produce useful work if thermodynamic process. In this case, the main thermodynamic parameters P also change, v and T. Thermodynamic process is a set of changes in the states of a thermodynamic system during its transition from one state to another.

We will only consider equilibrium thermodynamic processes occurring in equilibrium systems. equilibrium state The system is called the state when pressure and temperature are the same at all points of the system. The system, taken out of the state of equilibrium and left to itself at constant parameters of the environment, after some time will again come to an equilibrium state corresponding to these parameters. The process that goes through alternating equilibrium states of the system is called equilibrium process.

Otherwise, the system non-equilibrium. All real-time processes are, as a rule, non-equilibrium. The assumption of the existence of equilibrium systems is based on the fact that any system, taken out of the state of equilibrium and left to itself at constant parameters of the environment, will return to the equilibrium state after some time. Such a spontaneous (without external influence) return of the system to a state of equilibrium is called relaxation, and the time interval during which the real system returns to the state of equilibrium is called relaxation time. If the real process is slower than relaxation, then the process is equilibrium. For different processes and different parameters, the relaxation time is different. The internal processes that compensate for the imbalance when the state of the body changes and restore the thermodynamic equilibrium are the elementary processes of energy exchange during the collision of molecules.

It is interesting to note that the transformation of the energy of the translational motion of molecules into the energy of rotational motion and vice versa during the collision of molecules occurs very quickly. Thus, the pressure in the volume equalizes with the speed of sound (more than 340 m/s in air under normal physical conditions). Temperature is much slower. This is due to the fact that the transformation of the energy of the translational or rotational motion of molecules into vibrational energy with increasing temperature is relatively slow. In general, all energy exchange processes involving vibrational degrees of freedom of molecular motion require a relatively long time for their implementation.

Consider, for example, the process of compressing a gas in cylinder . If the time of displacement of the piston from one position to another significantly exceeds the relaxation time, then in the process of moving the piston, pressure and temperature will have time to equalize throughout the entire volume of the cylinder. This alignment is ensured by the continuous collision of molecules, as a result of which the energy supplied from the piston to the gas is fairly quickly and evenly distributed between them. If subsequent displacements of the piston will occur in a similar way, then the state of the system at each moment of time will be practically equilibrium.

Theoretically, an equilibrium process can be carried out only with an infinitely slow change in the states of the system and external conditions. In this sense, time as an active physical factor is not used in equilibrium processes.

Equation of state F (P, v, T) = 0 in the triaxial coordinate system Р, v and T represent a surface called thermodynamic surface. If we cut this surface (Fig. 1.8) with planes parallel to the coordinate axes, we get curves. For example, a section with a plane T = const gives a line of change in pressure depending on the volume in the coordinates P and v The described process is called isothermal.
In thermodynamics, a biaxial system with coordinates P and v(Fig. 1.9).