Thermodynamic process is called reversibleif it can pass both in direct and in the opposite direction; At the same time, after returning the system to its original state in environment And in the system itself no changes occur.

R awesome (quasistatic) The process is a continuous sequence of equilibrium states. Any point of such a process is an equilibrium state from which the system can go both in direct and in the opposite direction. Hence it follows that any equilibrium process is reversible.

Only thermodynamically equilibrium processes can be depicted graphically, because for the nonequilibrium system, the value of parameters, for example, temperature or concentration, volume is not the same, and for the entire system is an indefinite value. The processes occurring in such systems can be depicted graphically only approximately, according to the averaged parameter values.

An example of a reversible process of mechanics can be cited - absolutely elastic collision. If you replace time variable t. on - t., with an absolutely elastic strike, the initial and final velocities of bodies simply change roles. Newton's laws are reversible.

Reversible processes - idealization. All real processes in one degree or another are irreversible due to friction, diffusion, thermal conductivity. All transfer phenomena are irreversible processes. Heat itself can go only from hot to cold, but on the contrary. Another example of an irreversible process: absolutely inelastic collision, in which the mechanical energy is partially transformed or completely into heat.

Reversible processes are most economical, the system at such processes makes the maximum work, and the efficiency turns out to be maximal.

9) Carno cycle. Theorem Carno.

Let's try to create a heat machine when only reversible processes are used.

A reversible adiabatic process - heat transfer there is not at all; The work of external forces goes to increment internal energy Or vice versa, the operation of the system is performed at the expense of the internal energy of the system, and these processes are reversible.

But the heat transfer from the heater somehow must be carried out, otherwise, at the expense of which thermal energy, do we get useful work? Reversible process The heat transfer between two bodies can be carried out in an isothermal process if the temperature of both bodies is equal. Then it is indifferent, in which direction the flow of heat flow flows. But this process will be indefinitely slow.

In the carboy cycle (Fig. 8.10 and 8.11) perfect Gas. A cycle consisting of two adiabat (2-3 and 4-1) and two isotherms (1-2 and 3-4).

1-2 - isothermal expansion from volume V. 1 BE V. 2; In this case, gas is in contact with the heater at a temperature T. 1 ;

2-3 - adiabatic expansion from volume V. 2 BE V. 3; The final temperature of the gas is equal to the temperature of the cooler T. 2 ;

3-4 - isothermal compression from volume V. 3 BE V. four ; In this case, gas is in contact with the cooler at a temperature T. 2 ;

4-1 - adiabatic compression from volume V. 4 BE V. one ; The final temperature of the gas is equal to the temperature of the heater T. 1 .

For isothermal processes:

For adiabatic processes:

;

.

Then from the last two equalities:

Then the efficiency of the cycle of carno is:

.

The first part of the Carno Theorem is proved:

1) The efficiency of the carno cycle does not depend on the nature of the working fluid and is determined only by the temperatures of the heater and the cooler:

We formulate two other parts of the carno theorem, but we will prove them later.

2)The efficiency of any reversible cycle is not more than the efficiency of the carno cycle with the same heater temperatures and coolers:

. (8.39)

3)The efficiency of any irreversible cycle is less than the efficiency of the Carnot cycle with the same heater temperatures and the cooler:

. (8.40)

Entropy.

Determination of entropy

The concept of entropy was introduced by Clausius. Entropy is one of the functions of the state of the thermodynamic system. The status function is such a value that the values \u200b\u200bof which are unambiguously determined by the state of the system, and the change in the status function when the system is moving from one state to another is determined only by the initial and end states of the system and do not depend on the transition path.

Internal energy U.- status function. The internal energy of the perfect gas is equal, and its change is determined only by the initial and finite temperatures: . The value is the molar heat capacity of the perfect gas at a constant volume.

Quantity of heat Q. and work A. Not function functions are: they depend on the path of the system transition from the initial state to the final. For example, let the ideal gas moves from state 1 to state 2, having performed the isobaric process first first, then isochorn (Fig.8.12, and). Then the work performed for the whole process is equal . Now let it go out of 1 to 2 perfect gas, first performing a isochhore process, and then isobaric (Fig. 8.12, b.). Work with this transition is equal . Obviously. The magnitude of the work turned out to be different, although the initial and final state is the same. Since, according to the first law of thermodynamics, the amount of heat reported by the system is on the increment of internal energy and to work the system against external forces: then heat obtained by the system in processes a.and B.It will also be different, that is, the heat is also not a function function.

From the point of view of mathematics, the small increments of the values \u200b\u200bthat are not functions of the state will not be complete differentials, and it is necessary to use the designations: and. It turns out that for heat, the integrating factor is the inverse temperature: and the value equal to the ratio of the heat obtained to the absolute temperature is complete differential - this is the shown heat :. By definition of Clausius, the function of the state of the system, the differential of which in the reversible process is equal to the reduced heat, is entropy:

Properties of entropy

1) Entropy - the function of the system status, that is, in a closed system in the reversible process, when the system returns to its original state, complete entropy changes are zero:

. (8.42)

2) Entropy additive, that is, the entropy of the system is equal to the sum of the entropy of all its parts.

3) Entropy of a closed system does not decrease:

and for reversible processes and for irreversible.

The ratio (8.43) is called inequality Clausius and is one of the wording the second start of thermodynamics: entropy of a closed system remains constant if only reversible processes occur in it, and increases in the case of irreversible processes.

Consider a closed system consisting of two bodies with temperatures and. Let be the amount of heat obtained by the second body from the first. Then the amount of heat obtained by the first body is negative and equal. The complete increment of the entropy of the system of two bodies in the process of heat transfer is equal to the amount of changes to the entropy of two tel.

Similarly, in the first principle of thermodynamics, the function of the state is introduced - internal energy, in the second principle - the function of the state, called entropy (s) (from Greek entropia. - turn, transformation). Consideration of the change of this function led to the separation of all processes into two groups: reversible and irreversible (spontaneous) processes.

The process is called reversibleIf it can be carried out first in direct, and then in the opposite direction, and so that neither the system, nor in the environment there will be no change. Fully reversible process - abstractionBut many processes can be conducted in such conditions that their deviation from reversibility was very small. For this, Mo needs, in each of its infinitely small stages, the state of the system in which this process occurs will respond to the state of equilibrium.

Equilibrium condition – special condition The thermodynamic system in which it passes as a result of reversible or irreversible processes and can remain in it indefinitely long. Real processes can approach reversible, but for this they must be slow.

The process is called irreversible (natural, spontaneous, spontaneous)If it is accompanied by the scattering of energy, i.e., the uniform distribution between all the bodies of the system as a result of the heat transfer process.

As examples of irreversible processes, the following may be called:

freezing of supercooled fluid;

expansion of gas in vacuum space;

diffusion in the gas phase or in liquid.

The system in which an irreversible process occurred can be returned to its original state, but for this above the system you need to work.

The most real processes include irreversible processes, as they are always accompanied by work against friction forces, resulting in useless energy consumption, accompanied by scattering of energy.

To illustrate concepts, consider the perfect gas located in the cylinder under the piston. Let the initial pressure of the gas P 1 under its volume V 1 (Fig. 4.1).

Gas pressure is balanced by the piston of sand. The combination of equilibrium states is described by the equationpv \u003d const and is graphically portrayed with a smooth curve (1).

If you remove a certain amount of sand from the piston, then the gas pressure above the piston will decrease sharply (from A to B) only after which there will be an increase in the volume of gas to an equilibrium value (from B to C). The nature of this process is broken line 2. This line characterizes the dependence P \u003d f. (V) with an irreversible process.

Fig. 4.1. The dependence of the gas pressure on its volume during reversible (1) and irreversible processes (2, 3).

From the figure it is clear that when the gas expansion is reversible, the work performed by them (area under a smooth curve 1) is greater than with any irreversible expansion.

Thus, any thermodynamic process It is characterized by the highest possible size of the work if it is performed in reversible mode. You can come to a similar output if you consider the gas compression process. It should only be borne in mind that in this case the amount of work is a negative value (Fig. 4.1, broken 3).

Reversible and irreversible processes, Ways to change the state of the thermodynamic system. The process is called reversible if it allows the return of the system under consideration from the final state to the original one by the same sequence of intermediate states as in the direct process, but go through reverse order. At the same time, not only the system, but also the medium is returned to the original state. The reversible process is possible, if in the system, and in the environment it flows equally. It is assumed that equilibrium exists between separate parts The system under consideration and on the border with the environment. The reversible process is an idealized case achieved only with an infinitely slow change in thermodynamic parameters. The rate of establishment of equilibrium should be greater than the speed of the process under consideration. If it is impossible to find a way to return both the system, and the body in the environment in the original state, the process of changing the state of the system is irreversible.

Irreversible processes can occur spontaneously only in one direction; Such, viscous course and other. For chemical reaction Apply the concepts of thermodynamic and kinetic reversibility, which coincide only in close proximity to the state of equilibrium. R-│ A + in C + D Naz. kinetically reversible or bilateral if in these conditions products C and D can react with each other with the formation of starting materials A and B. At the same time, the speed of direct and reverse reactions, acc. where and speed-resistant, [a], [in], [s], [d] - current (activity), over time become equal and occurs, in which -Constant equilibrium,temperature-dependent. Thicatically irreversible (one-sided) are usually such reactions, during which at least one of the products are removed from the reaction zone (falls into the sediment, it will volatile or stand out as a lowly subsoous compound), as well as reactions accompanied by the release of a large amount of heat.

In practice, systems are often found in partial equilibrium, i.e. In equilibrium in relation to a certain kind of processes, whereas in general the system is not equilibrium. For example, a sample of hardened steel has spatial inhomogeneity and is a non-equilibrium system with respect to, however, in this sample, equilibrium mechanical deformation cycles may occur, since diffusion times and in characteristic of dozens of orders. Consequently, processes with relatively long time are kinetically inhibited and may not be taken into account during thermodynamic. Analysis of faster processes.

The irreversible processes are accompanied by dissipative effects, the essence of which is the production (generation) in the system as a result of the flow of the process under consideration. The simplest expression of the dissipation law is:

where average temperature, d I S-the production of entropy, - t. Naz. Uncompensated heat of Clausius (heat dissipation).

Reversible processes, being idealized, are not accompanied by dissipative effects. Microscopic theory of reversible and irreversible processes is developing in statistical thermodynamics. Systems in which irreversible processes proceed, study the thermodynamics of irreversible processes.

Lit.see at Art. Chemical thermodynamics. E. P. Agee.

Choose the first letter in the title of the article:

The second beginning of thermodynamics. Reversible and irreversible processes.

From formula (8.6.1) it can be seen that kp.d. The heat machine is less than one. There would be the best car, with KPD, equal to one. Such a car could completely turn into work all the warmth obtained from some body, without giving the refrigerator. Numerous experiments showed the impossibility of creating a similar machine. To this conclusion for the first time came the Sadi Carno in 1824. After studying the conditions of the heat machines, it proved that at least two sources of heat from the heat machine, it is necessary for the production of work. various temperatures. In the future, it was studied in detail by R. Clausius (1850) and V.Kelvin (1852), which formulated the second beginning of thermodynamics.

Clausius formulation: Heat cannot spontaneously move from less heated to a warmer body without any changes in the system. Those. The process is impossible, the only end result of which is the transmission of energy in the form of heat from the less heated body to a heated.

It does not follow from this definition that heat cannot be transmitted from less heated to a heated body. This happens in any refrigerators, But heat transfer here is not the end result, since it takes work.

Thomson's wording (Kelvin): It is impossible to transform all the warmth, taken from the body with a homogeneous temperature, without producing any other changes in the system state. Those. The process is impossible, the only end result of which is the transformation of the entire heat obtained from some body into it equivalent to it.

It does not follow here that the heat cannot be fully addressed to work. For example, with an isothermal process (du \u003d 0), the heat is fully referred to the work, but this result is not the only one, the ultimate, as the gas expansion still occurs.

It can be seen that the specified wording is equivalent.

The second principle of thermodynamics was finally formulated when all attempts were completed, all attempts to create an engine, which would add to work all the warmth obtained by it, without causing any other status changes to the system - eternal engine of the second kind. This is an engine having a kp. one hundred %. Therefore, another wording of the second start of thermodynamics: it is impossible to perpetuum mobile second-kind mobile, i.e. Such a periodically operating engine that would have received heat from one tank and turned this warmth completely into operation.

The second beginning of thermodynamics allows to divide all thermodynamic processes on reversible and irreversible. If, as a result of a process, the system moves from a state and to another state in and if it is possible to return it at least one way to its original state AND And moreover, so that any changes have happened in all other bodies, this process is called reversible. If it is impossible to do this, then the process is called irreversible. The reversible process could be carried out if the direct and opposite direction of its flow would be equal and equivalent.

Reversible processes are the processes flowing with very low speed, Ideally, infinitely slowly. In real conditions, the processes occur at a final rate, and therefore they can be considered reversible only with a certain accuracy. On the contrary, irreversibility is characteristic propertyarising from the very nature of thermal processes. An example of irreversible processes are all processes accompanied by friction, heat exchange processes at the final temperature difference, dissolution and diffusion processes. These all processes in the same direction proceed spontaneously, "by themselves", and to make each of these processes in the opposite direction it is necessary that some other compensating process occurred in parallel. Therefore, on earthly conditions, the events have a natural move, a natural direction.

The second beginning of the thermodynamicsdetermines the direction of leakage of thermodynamic processes and thereby gives an answer to the question of which processes in nature can occur spontaneously. It indicates the irreversibility of the transmission process of one form of energy - work to another - warmth. Work is the form of the transfer of energy of an ordered body movement as a whole; Heat - the form of the transfer of the energy of an unordered chaotic movement. Ordered movement can go into disordered spontaneously. Reverse transition is possible only if the work is performed by external forces.

Carno cycle.

Analyzing the operation of heat engines, carno concluded that the highest process is a reversible circular process consisting of two isotherms and two adiabat, as it is characterized by the highest coefficient useful action. This cycle received the name of the carno cycle.

Carno cycle- Direct circular process at which the system executed is the maximum work.

Let a certain system can enter into thermal contact with two thermal tanks, the temperatures of which T 1 and T 2, and the heat capacity is infinitely large (that is, the addition or extension of a certain amount of heat does not change the temperatures). We will assume that the system is the perfect gas located in a cylindrical vessel under the piston (Fig. 8.7.). We believe that the walls and piston are heat-proof.

Suppose first the system in a state with (p 1, v 1, t 1) is driven by thermal contact with the first tank. When the heat system is reported, Q 1 is performed against external forces, numerically equal to Q 1, gas expands to volume V 2.

Then the cylinder is rearranged on an insulating stand. Gaza is given the opportunity to continue to expand to volume V 3 so that the temperature is t 2.

We translate the cylinder with the piston in thermal contact with the second tank with the temperature T 2, and the external bodies make the Q 2 over the system, so the volume becomes V 4.

Re-insulating the system and reduce the volume to the initial value V 1, so the temperature will increase from T 2 to T 1.

If all four processes are reversible, then all our reasoning is valid, and the system will really return to the initial state with (P 1, V 1, T 1).

Thus, the described cycle consists of two isothermal (1®2 and 3®4) and two adiabatic extensions and compressions (2®3 and 4®1) (see Fig. 8.8.). The car that makes the carno cycle is called the perfect thermal machine.

Work performed during isothermal expansion:

; A 1 \u003d Q 1. (8.8.1)

With adiabatic expansion, the work is made due to loss of the internal energy of the system, since Q '\u003d 0:

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Reversible process (That is, equilibrium) - a thermodynamic process, which can pass both in direct and in the opposite direction, passing through the same intermediate states, and the system returns to its original state without energy costs, and macroscopic changes remain in the environment.

The reversible process can be at any time to proceed in the opposite direction, changing any independent variable to an infinitely small value.

Reversible processes give the greatest work. It is impossible to get a lot of work from the system. This gives reversible processes theoretical importance. In practice, the reversible process is impossible to implement. It proceeds endlessly slowly, and you can only get closer to it.

It should be noted that the thermodynamic reversibility of the process differs from chemical reversibility. Chemical reversibility characterizes the direction of the process, and the thermodynamic is the method of its conduct.

The concepts of equilibrium state and reversible process play a large role in thermodynamics. All the quantitative conclusions of thermodynamics are applicable only to equilibrium states and reversible processes. In a state of chemical equilibrium, the rate of direct reaction is equal to the rate of reverse reaction!

Examples

Baking pie - an irreversible process. Hydrolysis of salts is a reversible process.

see also

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Links

• socrates.berkeley.edu/~ashvinv/phy211/lecture3.pdf.
• www.Britannica.com/ebChecked/Topic/500473/reversibility

Excerpt characterizing a reversible process

- Do you think how? He from all ranks are scored.
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"After all, then wisely, my brothers," the one who was surprised in whiteness was surprised, "the men were told under Mozhaisk, as they were to clean the battered, where she was, so that, he says, read the month lying the dead. Well, says, lies, says their own, how white paper, clean, nor blue powder smells.
- Well, from the cold, what about - asked one.
- Eca you're smart! By cold! It was hot because it was. You can also not rubley too. And then, says, come to our, all, says, rotted in the worms. So, he says, we will asshide the headscarves, yes, the title face, and tested; urine no. And their own, says how white paper; Neither blue powder smells.
Everyone was silent.
"Should, from food," said Feldfelf, "the gentleman's food erupted."
No one objected.
- the man told that this one, under Mozhaisk, where she was that, they were angry with ten villages, twenty days were drove, did not take all the dead, then. Wolves of these what, says ...
"That suffer was real," said the old soldier. - just was what to remember; And then everything after that ... so, only the people of torment.
- And that, uncle. The day before yesterday we came, so where they do not allow themselves. Vivid rifles left. On the knees. Pardon - says. So, only an example one. They told the Polyon itself, the boards took two times. Words do not know. I will take away: here on those in the hands will catch the bird, fly away, and it will fly away. And there is no position too.