According to one of the formulations of the second law of thermodynamics. Second law of thermodynamics

Spontaneous (spontaneous) processes described by the following characteristics:

1. All natural spontaneous processes proceed in one direction, that is, they have a one-way direction. For example, heat from a hot body passes to a cold one; gases tend to occupy the largest volume.

2. Part of the energy passes into heat, i.e., the system passes from an ordered state into a state with random thermal motion of particles.

3. Spontaneous processes can be used to produce useful work. As the transformation progresses, the system loses its ability to do work. In the final state of equilibrium, it has the smallest amount of energy.

4. The system cannot be returned to its original state without making any changes in itself or in the environment. All spontaneous processes are thermodynamically irreversible.

5. In a spontaneous process, the initial state is less probable compared to each successive state and the least probable compared to the final one.

Non-spontaneous processes proceed at the cost of work; in this case, the system moves away from the equilibrium state (for example, gas compression, electrolysis).

Second law of thermodynamics is a postulate. It has a statistical character and is applicable to systems of a large number of particles.

The second law of thermodynamics has the following formulations:

1. Heat cannot spontaneously transfer from a less heated body to a more heated one.

2. A process is impossible, the only result of which is the conversion of heat into work.

3. A perpetual motion machine of the second kind is impossible. The heat of the coldest of the bodies involved in the process cannot serve as a source of work.

Analytical expression of the second law of thermodynamics and its justification using the Carnot cycle. The essence of the expression of the second law of thermodynamics is the connection between the spontaneity of the process and the increase in entropy. This expression follows from the consideration of the question of the theoretical completeness of the transformation of heat into work in a reversible Carnot cycle.

The cycle consists of four processes:

AB- isothermal expansion due to heat Q1, connected to the gas at a temperature T 1;

sun- adiabatic expansion;

SD- isothermal compression at temperature T 2, in this process the gas loses heat Q2;

YES- adiabatic compression to the initial state.

The heat absorbed (or released) during the isothermal expansion (or compression) of one mole of an ideal gas is equal to the work

With adiabatic expansion (or contraction)

Applying these equations to the corresponding cycle processes leads to an expression for the thermodynamic efficiency (efficiency): . (4.3)

Equation (4.3) is a mathematical expression of the second law of thermodynamics.

Because T1‹ T2, then η < one.

According to Carnot's theory, the replacement of an ideal gas by any other substance will not lead to a change in efficiency. the Carnot cycle. Replacing the Carnot cycle with any other cycle will lead to lower efficiency. (the Clasius-Carnot theorem). Thus, even in the case of an ideal heat engine converting heat into work cannot be complete.

The expression of the second law of thermodynamics allows us to introduce the concept of entropy, with the help of which the essence of the law is revealed in a convenient and general form.

Let's change the expression (4.3):

on the . (4.4)

The ratio is called reduced heat. Equation (4.4) shows that the algebraic sum of the reduced heats over the reversible Carnot cycle is zero.

For an infinitesimal reversible Carnot cycle

where is the elementary reduced heat.

Any cycle can be replaced by a set of infinitely small Carnot cycles: .

In the limit, this amount will turn into.

In the theory of integrals, it is proved that if the integral over a closed loop is equal to zero, then the integrand is the total differential of some function of the parameters that determine the state of the system.

where S- this is entropy, such a function of the state of the system, the total differential of which in a reversible process is equal to the ratio of an infinitesimal amount of heat to temperature.

The concept of "entropy" was introduced by Clausius (1850) . This expression is a mathematical expression of the second law of thermodynamics for reversible processes.

The change in entropy in a reversible process is equal to the change in entropy in an irreversible process, i.e. . Let us compare the heats of reversible and irreversible processes. According to the first law of thermodynamics . Internal energy U is a function of the state of the system, so . Maximum work is done in a reversible process, so

In general, for reversible and irreversible processes The second law of thermodynamics has the following mathematical expression:

Here dS = const, and only the right side of the equation changes, i.e. the value of the heat value. Entropy units: [ S] = J/mol K.

The combined equation of the first and second law of thermodynamics:

Calculation of the change in the entropy of an ideal gas.

We express the change in internal energy

Dividing equation (4.6) by T, we define the change in entropy:

(4.7)

From the ideal gas equation: it follows that . Then, after substituting this relation into (4.7):

(4.8)

We integrate expression (4.8) as and obtain equation for calculating the change in entropy of an ideal gas:

(4.9)

Isothermal process, : , (4.10)

since then . (4.11)

Isochoric process, : . (4.12)

Isobaric process, : . (4.13)

Adiabatic process, : . (4.14)

Planck's postulate has the following formulation: at absolute zero, the entropy of correctly formed crystals of pure substances is equal to zero. The postulate makes it possible to calculate the absolute value of entropy if the heats of phase transitions are known, and if the heat capacities of a substance in various aggregate states are known.

How is energy generated, how is it converted from one form to another, and what happens to energy in a closed system? All these questions can be answered by the laws of thermodynamics. The second law of thermodynamics will be discussed in more detail today.

Laws in everyday life

Laws govern daily life. Road laws say you must stop at stop signs. The government demands to give part of their salary to the state and the federal government. Even scientific ones are applicable to everyday life. For example, the law of gravity predicts a rather poor outcome for those who try to fly. Another set of scientific laws that affect everyday life are the laws of thermodynamics. So, a number of examples can be given to see how they affect everyday life.

First law of thermodynamics

The first law of thermodynamics states that energy cannot be created or destroyed, but it can be transformed from one form to another. This is also sometimes referred to as the law of conservation of energy. So how does this apply to everyday life? Well, take, for example, the computer you are using now. It feeds on energy, but where does this energy come from? The first law of thermodynamics tells us that this energy couldn't come from the air, so it came from somewhere.

You can track this energy. The computer is powered by electricity, but where does the electricity come from? That's right, from a power plant or hydroelectric power plant. If we consider the second, then it will be associated with a dam that holds back the river. The river has a connection with kinetic energy, which means that the river is flowing. The dam converts this kinetic energy into potential energy.

How does a hydroelectric power plant work? Water is used to turn the turbine. When the turbine rotates, a generator is set in motion, which will create electricity. This electricity can be run entirely in wires from the power plant to your home, so that when you plug the power cord into an electrical outlet, the electricity enters your computer so it can work.

What happened here? There was already a certain amount of energy that was associated with the water in the river as kinetic energy. Then it turned into potential energy. The dam then took that potential energy and turned it into electricity, which could then enter your home and power your computer.

Second law of thermodynamics

By studying this law, one can understand how energy works and why everything moves towards possible chaos and disorder. The second law of thermodynamics is also called the law of entropy. Have you ever wondered how the universe came into being? According to the Big Bang Theory, before everything was born, a huge amount of energy gathered together. The Universe appeared after the Big Bang. All this is good, but what kind of energy was it? At the beginning of time, all the energy in the universe was contained in one relatively small place. This intense concentration represented a huge amount of what is called potential energy. Over time, it spread over the vast expanse of our universe.

On a much smaller scale, the reservoir of water held by the dam contains potential energy, since its location allows it to flow through the dam. In each case, the stored energy, once released, spreads out and does so without any effort being made. In other words, the release of potential energy is a spontaneous process that occurs without the need for additional resources. As energy is distributed, some of it is converted into useful energy and performs some work. The rest is converted into unusable, simply called heat.

As the universe continues to expand, it contains less and less usable energy. If less useful is available, less work can be done. Since the water flows through the dam, it also contains less useful energy. This decrease in usable energy over time is called entropy, where entropy is the amount of unused energy in a system, and a system is simply the collection of objects that make up a whole.

Entropy can also be referred to as the amount of randomness or chaos in an organization without organization. As usable energy decreases over time, disorganization and chaos increase. Thus, as the accumulated potential energy is released, not all of this is converted into useful energy. All systems experience this increase in entropy over time. This is very important to understand, and this phenomenon is called the second law of thermodynamics.

Entropy: Randomness or Defect

As you may have guessed, the second law follows the first, which is commonly referred to as the law of conservation of energy, and states that energy cannot be created and cannot be destroyed. In other words, the amount of energy in the universe or any system is constant. The second law of thermodynamics is commonly referred to as the law of entropy, and it holds that as time passes, energy becomes less useful and its quality decreases over time. Entropy is the degree of randomness or defects that a system has. If the system is very disordered, then it has a large entropy. If there are many faults in the system, then the entropy is low.

In simple terms, the second law of thermodynamics states that the entropy of a system cannot decrease over time. This means that in nature things go from a state of order to a state of disorder. And it's irreversible. The system will never become more orderly on its own. In other words, in nature, the entropy of a system always increases. One way to think about it is your home. If you never clean and vacuum it, then pretty soon you will have a terrible mess. Entropy has increased! To reduce it, it is necessary to use energy to use a vacuum cleaner and a mop to clean the surface of dust. The house won't clean itself.

What is the second law of thermodynamics? The formulation in simple words says that when energy changes from one form to another, matter either moves freely, or the entropy (disorder) in a closed system increases. Differences in temperature, pressure, and density tend to level off horizontally over time. Due to gravity, density and pressure do not equalize vertically. The density and pressure at the bottom will be greater than at the top. Entropy is a measure of the spread of matter and energy wherever it has access. The most common formulation of the second law of thermodynamics is mainly associated with Rudolf Clausius, who said:

It is impossible to build a device that does not produce another effect than the transfer of heat from a body of lower temperature to a body of higher temperature.

In other words, everything tries to maintain the same temperature over time. There are many formulations of the second law of thermodynamics that use different terms, but they all mean the same thing. Another Clausius statement:

Heat itself does not proceed from a colder to a hotter body.

The second law only applies to large systems. It concerns the likely behavior of a system in which there is no energy or matter. The larger the system, the more likely the second law is.

Another wording of the law:

The total entropy always increases in a spontaneous process.

The increase in entropy ΔS during the course of the process must exceed or be equal to the ratio of the amount of heat Q transferred to the system to the temperature T at which heat is transferred.

Thermodynamic system

In a general sense, the formulation of the second law of thermodynamics in simple terms states that temperature differences between systems in contact with each other tend to equalize and that work can be obtained from these non-equilibrium differences. But in this case, there is a loss of thermal energy, and the entropy increases. Differences in pressure, density, and temperature tend to equalize if given the opportunity; density and pressure, but not temperature, depend on gravity. A heat engine is a mechanical device that provides useful work due to the difference in temperature between two bodies.

A thermodynamic system is one that interacts and exchanges energy with the area around it. Exchange and transfer must occur in at least two ways. One way should be heat transfer. If a thermodynamic system is "in equilibrium", it cannot change its state or status without interacting with its environment. Simply put, if you are in balance, you are a "happy system", there is nothing you can do. If you want to do something, you must interact with the outside world.

The second law of thermodynamics: the irreversibility of processes

It is impossible to have a cyclic (repeating) process that completely converts heat into work. It is also impossible to have a process that transfers heat from cold objects to warm objects without using work. Some energy in a reaction is always lost to heat. Also, the system cannot convert all of its energy into work energy. The second part of the law is more obvious.

A cold body cannot heat a warm body. Heat naturally tends to flow from warmer to cooler areas. If heat goes from cooler to warmer it is contrary to what is "natural" so the system has to do some work to make it happen. in nature - the second law of thermodynamics. This is perhaps the most famous (at least among scientists) and important law of all science. One of his statements:

The entropy of the universe tends to a maximum.

In other words, entropy either stays the same or gets bigger, the entropy of the universe can never decrease. The problem is that this is always true. If you take a bottle of perfume and spray it in a room, then soon the fragrant atoms will fill the entire space, and this process is irreversible.

Relationships in thermodynamics

The laws of thermodynamics describe the relationship between thermal energy or heat and other forms of energy, and how energy affects matter. The first law of thermodynamics states that energy cannot be created or destroyed; the total amount of energy in the universe remains unchanged. The second law of thermodynamics is about the quality of energy. It states that as energy is transferred or converted, more and more usable energy is lost. The second law also states that there is a natural tendency for any isolated system to become more disordered.

Even when order increases at a certain location, when you take into account the entire system, including the environment, there is always an increase in entropy. In another example, crystals may form from a salt solution when water is evaporated. Crystals are more ordered than salt molecules in solution; however, evaporated water is much more disordered than liquid water. The process, taken as a whole, results in a net increase in disorder.

Work and energy

The second law explains that it is impossible to convert thermal energy into mechanical energy with 100 percent efficiency. An example is a car. After the process of heating the gas to increase its pressure to drive the piston, there is always some heat left in the gas that cannot be used to perform any additional work. This waste heat must be discarded by transferring it to a radiator. In the case of a car engine, this is done by extracting the spent fuel and air mixture into the atmosphere.

In addition, any device with moving parts creates friction that converts mechanical energy into heat, which is usually unusable and must be removed from the system by transferring it to a radiator. When a hot body and a cold body are in contact with each other, thermal energy will flow from the hot body to the cold body until they reach thermal equilibrium. However, the heat will never return the other way; the temperature difference between two bodies will never spontaneously increase. Moving heat from a cold body to a hot body requires work to be done by an external energy source such as a heat pump.

The fate of the universe

The second law also predicts the end of the universe. This is the ultimate level of disorder, if there is constant thermal equilibrium everywhere, no work can be done and all energy will end up as the random movement of atoms and molecules. According to modern data, the Metagalaxy is an expanding non-stationary system, and there can be no talk of the heat death of the Universe. Thermal death is a state of thermal equilibrium in which all processes cease.

This position is erroneous, since the second law of thermodynamics applies only to closed systems. And the universe, as you know, is limitless. However, the very term “heat death of the Universe” is sometimes used to refer to a scenario for the future development of the Universe, according to which it will continue to expand indefinitely into the darkness of space until it turns into scattered cold dust.

Basic provisions of the second law of thermodynamics

The first law of thermodynamics, being a special case of the general law of conservation and transformation of energy, states that heat can be converted into work, and work into heat, without establishing the conditions under which these transformations are possible.

He does not at all consider the question of the direction of the thermal process, and without knowing this direction, it is impossible to predict its nature and results.

For example, the first law does not solve the question of whether the transfer of heat from a heated body to a cold one or vice versa will take place. Everyday observations and experiments show that heat can transfer by itself only from heated bodies to colder ones. The transfer of heat from a heated body to the medium will occur until complete temperature equilibrium with the environment. It is only through the expenditure of work that the direction of heat movement can be changed.

This property of heat sharply distinguishes it from work.

Work, like all other types of energy involved in any process, is easily and completely converted into heat. The complete conversion of work into heat was known to man in ancient times, when he made fire by rubbing two pieces of wood. The processes of converting work into heat occur continuously in nature: friction, impact, braking, etc.

Heat behaves quite differently, for example, in heat engines. The transformation of heat into work occurs only when there is a temperature difference between the heat source and the heat sink. However, all heat cannot be converted into work.

It follows from what has been said that there is a profound difference between the conversion of heat into work and vice versa. The law that allows you to indicate the direction of the heat flow and establishes the maximum possible limit for the conversion of heat into work in heat engines is a new law, gained from experience. This is the second law of thermodynamics, which is of general importance for all thermal processes. The second law of thermodynamics is not limited to technology; It is used in physics, chemistry, biology, astronomy, etc.

In 1824, Sadi Carnot, a French engineer and scientist, in his discussion of the driving force of fire, outlined the essence of the second law.

In the 50s of the last century, Clausius gave the most general and modern formulation of the second law of thermodynamics in the form of the following postulate: Heat cannot transfer from a cold body to a hotter one by itself by a free process (without compensation)". The postulate of Clausius should be considered as an experimental law, obtained from observations of the surrounding nature. Clausius' conclusion was made in relation to the field of technology, but it turned out that the second law in relation to physical and chemical phenomena is also correct. The postulate of Clausius, like all other formulations of the second law, expresses one of the basic, but not absolute, laws of nature, since it was formulated in relation to objects that have finite dimensions in the earthly conditions around us.

Simultaneously with Clausius in 1851, Thomson expressed another formulation of the second law of thermodynamics, from which it follows that not all the heat received from the heat source can go into work, but only some of it.

Part of the heat must go to the heat sink.

Therefore, to obtain work, it is necessary to have a source of heat with a high temperature, or heat sink, and a low temperature heat source, or heat receiver. In addition, Thomson's postulate shows that it is not possible to build a perpetual motion machine that would create work by using only the internal energy of the seas, oceans, and air. This position can be formulated as the second law of thermodynamics: "Implementation of a perpetual motion machine of the second kind is impossible." By a perpetual motion machine of the second kind is meant such an engine that is capable of completely converting into work all the heat received from only one source.

In addition to the above, there are several more formulations of the second law of thermodynamics, which, in essence, do not introduce anything new and therefore are not given.

Entropy.

The Second Law of Thermodynamics, like the First Law (the Law of Conservation of Energy), has been established empirically. It was first formulated by Clausius: "heat itself passes only from a body with a higher temperature to a body with a lower temperature and cannot spontaneously move in the opposite direction."

Another wording: all spontaneous processes in nature go with increasing entropy. (Entropy- a measure of randomness, disorder of the system). Consider a system of two contacting bodies with different temperatures. Warm will move from a body with a higher temperature to a body with a lower temperature until the temperatures of both bodies are equal. In this case, a certain amount will be transferred from one body to another heat dQ. But entropy at the same time, the first body will decrease by a smaller amount than it will increase for the second body, which takes warmth, since, by definition, dS=dQ/T (temperature in the denominator!). That is, as a result of this spontaneous process entropy system of two bodies will become greater than the sum entropy these bodies before the start of the process. In other words, spontaneous process transfer of heat from a body with a high temperature to a body with a lower temperature entropy system of these two bodies has increased!

The most important properties of the entropy of closed systems:

a) The entropy of a closed system performing a reversible Carnot cycle does not change:

ΔS arr =0, S=const.

b) The entropy of a closed system performing an irreversible Carnot cycle increases:

ΔS unmod >0.

c) The entropy of a closed system does not decrease for any processes occurring in it: ΔS≥0.

With an elementary change in the state of a closed system, the entropy does not decrease: dS≥0. The equal sign refers to reversible processes, and the inequality sign to irreversible ones. Point c) is one of the formulations of the second law (beginning) of thermodynamics. For an arbitrary process occurring in a thermodynamic system, the relation is true:

where T is the temperature of the body that reports. Thermodynamic system energy δQ in the process of an infinitesimal change in the state of the system. Using the first law of thermodynamics for δQ, the previous inequality can be rewritten in a form combining the first and second laws of thermodynamics: TdS ≥ dU+δA.

Entropy properties.

1. So, entropy is a state function. If the process is carried out along the adiabats, then the entropy of the system does not change. So adiabats are also isentropes. Each "higher" located adiabat (isoentrope) corresponds to a greater value of entropy. It is easy to verify this by carrying out an isothermal process between points 1 and 2 lying on different adiabats (*see Fig.). In this process, T=const, so S2-S1=Q/T. For an ideal gas, Q is equal to the work A performed by the system. And since A>0, it means S 2 >S 1. Thus, knowing what the adiabatic system looks like. It is easy to answer the question about the increase in entropy during any process between equilibrium states 1 and 2 of interest to us. Entropy is an additive quantity: the entropy of a macrosystem is equal to the sum of the entropies of its individual parts.

3. One of the most important properties of entropy is that the entropy of a closed (ie thermally insulated) macrosystem does not decrease - it either increases or remains constant. If the system is not closed, then its entropy can both increase and decrease.

The principle of increasing entropy of closed systems is another formulation of the second law of thermodynamics. The magnitude of the increase in entropy in a closed macrosystem can serve as a measure of the irreversibility of the processes occurring in the system. In the limiting case, when the processes are reversible, the entropy of a closed macrosystem does not change.

The difference ΔS of the entropy in two states of the system has a physical meaning. To determine the change in entropy in the case of an irreversible transition of the system from one state to another, you need to come up with some kind of reversible process that connects the initial and final states, and find the reduced heat received by the system during such a transition.

Rice. 3.12.4 - Irreversible process of gas expansion "into the void" in the absence of heat exchange

Only the initial and final states of the gas in this process are in equilibrium, and they can be depicted on the diagram (p, V). Points (a) and (b) corresponding to these states lie on the same isotherm. To calculate the entropy change ΔS, one can consider a reversible isothermal transition from (a) to (b). Since, during isothermal expansion, the gas receives a certain amount of heat from the surrounding bodies Q > 0, we can conclude that the entropy increased during the irreversible expansion of the gas: ΔS > 0.

Another example of an irreversible process is heat transfer at a finite temperature difference. On fig. 3.12.5 shows two bodies enclosed in an adiabatic shell. Initial body temperatures T 1 and T 2< T 1 . При теплообмене температуры тел постепенно выравниваются. Более теплое тело отдает некоторое количество теплоты, а более холодное – получает. Приведенное тепло, получаемое холодным телом, превосходит по модулю приведенное тепло, отдаваемое горячим телом. Отсюда следует, что изменение энтропии замкнутой системы в необратимом процессе теплообмена ΔS > 0.

Entropy growth is a common property of all spontaneous irreversible processes in isolated thermodynamic systems. With reversible processes in isolated systems, the entropy does not change: ΔS≥0. This relation is called the law of increasing entropy. In any process occurring in thermodynamic isolated systems, the entropy either remains unchanged or increases.

Thus, entropy indicates the direction of spontaneous processes. An increase in entropy indicates that the system is approaching a state of thermodynamic equilibrium. In the state of equilibrium, entropy takes on a maximum value. The law of increasing entropy can be taken as another formulation of the second law of thermodynamics.

In 1878, L. Boltzmann gave a probabilistic interpretation of the concept of entropy. He proposed to consider entropy as a measure of statistical disorder in a closed thermodynamic system. All spontaneous processes in a closed system, bringing the system closer to the state of equilibrium and accompanied by an increase in entropy, are directed towards increasing the probability of the state.

Any state of a macroscopic system containing a large number of particles can be realized in many ways. The thermodynamic probability W of a system state is the number of ways in which a given state of a macroscopic system can be realized, or the number of microstates realizing a given macrostate. By definition, the thermodynamic probability is W >> 1.

For example, if there is 1 mol of gas in a vessel, then a huge number N of ways of placing a molecule in two halves of the vessel is possible: where is Avogadro's number. Each of them is a microstate.

Only one of the microstates corresponds to the case when all molecules are collected in one half (for example, the right one) of the vessel. The probability of such an event is practically zero. The largest number of microstates corresponds to the equilibrium state, in which the molecules are evenly distributed throughout the volume. Therefore, the equilibrium state is the most probable. On the other hand, the equilibrium state is the state of the greatest disorder in the thermodynamic system and the state with maximum entropy.

According to Boltzmann, the entropy S of the system and the thermodynamic probability W are related as follows: S=klnW, where k = 1.38·10 –23 J/K is Boltzmann's constant. Thus, entropy is determined by the logarithm of the number of microstates with which a given macrostate can be realized. Therefore, entropy can be considered as a measure of the probability of the state of a thermodynamic system. The probabilistic interpretation of the second law of thermodynamics allows a spontaneous deviation of the system from the state of thermodynamic equilibrium. Such deviations are called fluctuations. In systems containing a large number of particles, significant deviations from the equilibrium state are extremely unlikely.

Circular thermodynamic processes, or cycles

In the thermodynamic processes considered earlier, to study the issues of obtaining work either as a result of the supplied heat, or as a result of a change in the internal energy of the working fluid, or simultaneously as a result of both. With a single expansion of the gas in the cylinder, only a limited amount of work can be obtained. Indeed, in any process of rhenium gas in the cylinder, there will still come a moment when the temperature and pressure of the working fluid become equal to the temperature and pressure of the environment, and the work will stop there.

Therefore, in order to re-obtain work, it is necessary to return the working body to its original state during the compression process.

It follows from Figure 8 that if the working fluid expands along the 1-3-2 curve, then it produces the work depicted on the pv-diagram pl. 13245. Upon reaching point 2, the working fluid must be returned to its initial state (at point 1) so that it can again perform work. The process of returning the body to its initial state can be carried out in three ways.

Figure 8 - Circular processes.

1. The 2-3-1 compression curve is the same as the 1-3-2 expansion curve. In such a process, all the work obtained during the expansion (pl. 13245) is equal to the work of compression (pl. 23154) and the positive work is equal to zero. The 2-6-1 compression curve is above the 1-3-2 expansion line; .at the same time, more work is expended on compression (plot 51624) than it will be received during expansion (plot 51324).

The compression curve-2-7-1 is located under the expansion line 1-3-2. In this circular process, the work of expansion (square 51324) will be greater than the work of compression (square 51724). As a result, positive work will be given outward, represented by square. 13271 inside a closed line of a circular process, or cycle.

By repeating the cycle an unlimited number of times, any amount of work can be obtained due to the input heat.

A cycle that produces positive work is called direct cycle or heat engine cycle; in it, the work of expansion is greater than the work of compression. The cycle that consumes work is called reverse, in it the work of compression is greater than the work of expansion. Refrigeration units operate in reverse cycles.

Cycles are reversible and irreversible. A cycle consisting of equilibrium reversible processes is called reversible. The working fluid in such a cycle should not be subjected to chemical changes.

If at least one of the processes included in the cycle is irreversible, then the whole cycle will be irreversible.

The results of studies of ideal cycles can be transferred to real, irreversible processes of real machines by introducing experimental correction factors.

Thermal efficiency and coefficient of performance of cycles

The study of any reversible cycle proves that for the implementation it is necessary at each point of the direct process to supply heat from the heat emitters to the working fluid at an infinitely small temperature difference and remove heat from the working fluid to the heat sinks also at an infinitely small temperature difference. In this case, the temperature of two neighboring heat sources must differ by an infinitesimal value, since otherwise, with a finite temperature difference, the processes of heat transfer will be irreversible:

On the path 1-3-2 (Figure 8), the working fluid performs specific work of expansion, numerically equal to square. 513245, due to the specific amount of heat received from the heat emitters, and partly due to its internal energy. On the way 2-7-1, specific work of compression is expended, numerically equal to square. 427154, part of which in the form of a specific amount of heat is removed to the heat sinks, and the other part is spent on increasing the internal energy of the working fluid to the initial state. As a result of the implementation of the direct cycle, positive specific work will be given outward, equal to the difference between the work of expansion and contraction. This work .

The ratio between specific quantities of heat and and positive specific work is determined by the first law of thermodynamics.

Since in the cycle the final state of the body coincides with the initial state, the internal energy of the working body does not change and therefore

The ratio of the specific amount of heat converted into positive specific work in one cycle to the entire specific amount of heat supplied to the working fluid is called t thermal efficiency of direct

cycle:

The value is an indication of the perfection of the heat engine cycle. The more , the greater part of the supplied heat is converted into useful work. Thermal efficiency value cycle is always less than one and could be equal to one if or , which cannot be done.

The resulting equation (62) shows that it is impossible to completely convert all the heat supplied to the working fluid in the cycle into work without removing a certain amount of heat to the heat sink.

Thus, Carnot's main idea turned out to be correct, namely: in a closed circular process, heat can turn into mechanical work only if there is a temperature difference between heat emitters and heat sinks. The greater this difference, the higher the efficiency. heat engine cycle.

Consider now the reverse cycle, which runs in the counterclockwise direction and is depicted on the pv-diagram pl. 13261. The expansion of the working fluid in this cycle takes place at a lower temperature than the compression, and the work of expansion (pl. 132451) is less than the work of compression (pl. 162451). Such a cycle can be carried out only with the expenditure of external work.

In the reverse cycle, heat is supplied from the heat sinks to the working fluid and specific work is expended, turning into an equal amount of heat, which together are transferred to the heat sinks:

Without the expenditure of work by itself, such a transition is impossible.

The degree of perfection of the reverse cycle is determined by the so-called cycle factor.

The coefficient of performance shows how much heat is taken away from the heat sink at the expense of one unit of work. Its value is usually greater than one.

Carnot cycles.

Direct reversible Carnot cycle

A reversible cycle carried out between two heat sources of constant temperature must consist of two reversible isothermal and two reversible adiabatic processes.

This cycle was first considered by Sadi Carnot in his work “Reflections on the driving force of fire and on machines capable of developing this force”, published in 1824. For a better understanding of the procedure for implementing this cycle, imagine a heat engine, the cylinder of which can be as needed both absolutely thermally conductive and absolutely non-thermally conductive. Let in the first position of the piston the initial parameters of the working fluid and the temperature be equal to the temperature of the heat transfer device. If at this moment the cylinder is absolutely thermally conductive and if it is brought into contact with a heat sink of infinitely large energy capacity, imparting heat to the working fluid according to the 1-2 isotherm, then the gas will expand to point 2 and do work. Point 2 parameters: From point 2 the cylinder must be absolutely non-thermal. The working fluid with temperature T 1 , expanding along the adiabatic 2-3 to the temperature of the heat sink T 2 , will do the work. Point 3 parameters: . From point 3 we make the cylinder absolutely thermally conductive. Compressing the working fluid along the 3-4 isotherm, we simultaneously remove heat to the heat sink. At the end of isothermal compression, the parameters of the working fluid will be . From point 4 in an absolutely non-thermal-conducting cylinder, the working fluid returns to its original state by the adiabatic compression process 4-1.

Thus, for the entire cycle, heat was imparted to the working fluid from the heat sink and heat was removed to the heat sink.

Thermal efficiency cycle

The heat supplied by the isotherm 1-2 is determined as follows:

The absolute value of the removed heat according to the isotherm 3-4 is found as follows:

Substituting the found values ​​and into the equation for thermal efficiency, we obtain

For the adiabatic process of expansion and contraction, respectively, we have

and

Therefore, the thermal efficiency equation Carnot cycle after cancellation takes the form

Thermal efficiency reversible Carnot cycle depends only on the absolute temperatures of the heat sink and heat sink. It will be the greater, the higher the temperature of the heat sink and the lower the temperature of the heat sink. Thermal efficiency the Carnot cycle is always less than one, since to obtain an efficiency equal to one, it is necessary that T 2 =0 or T 1 = ∞, which is not feasible. Thermal efficiency the Carnot cycle does not depend on the nature of the working fluid and at T 2 -T 1 is equal to zero, that is, if the bodies are in thermal equilibrium, then it is impossible to convert heat into work.

Thermal efficiency the Carnot cycle is the most important
compared to efficiency any cycle carried out in one and
the same temperature range. Therefore the comparison
thermal efficiency any cycle and Carnot cycle allows you to do
a conclusion on the degree of perfection of the use of heat in a machine operating according to a given cycle.

In real engines, the Carnot cycle does not occur due to practical
difficulties. However, the theoretical and practical significance of the Carnot cycle is very great. It serves as a benchmark in evaluating the excellence of any heat engine cycles. .

The reversible Carnot cycle, carried out in the temperature range T 1 and T 2 , is depicted on the Ts-diagram by a rectangle 1234 (Figure 9).

Figure 9 - Reversible Carnot cycle.

Reverse Reversible Carnot Cycle

The Carnot cycle can proceed not only in the forward but also in the opposite direction. Figure 10 shows the inverse Carnot cycle. The cycle consists of reversible processes and is generally reversible.

Figure 10 - Reverse Carnot cycle.

The working fluid from the starting point 1 expands along the adiabatic 1-4 without heat exchange with the environment, while the temperature T 1 is issued to T 2 . This is followed by further expansion of the gas along the isotherm 4-3 with the supply of heat, which is taken from the source with a low temperature T 2 . This is followed by adiabatic compression 3-2 with an increase in temperature from T 2 to T 1 . During the latter process, 2-1 isothermal compression takes place, during which heat is removed to the heat sink at high temperature.

Considering the reverse cycle as a whole, it can be noted that the expended external work of compression is greater than the work of expansion by the value of pl. 14321 inside a closed cycle line. This work is converted into heat and transferred together with heat to a source with temperature T 1 . Thus, having spent specific work on the implementation of the reverse cycle, it is possible to transfer from the heat sink to the heat sink

units of heat. In this case, the heat received by the heat sink is equal to

A machine that works on a reverse cycle is called a refrigeration machine. Considering the inverse Carnot cycle, we can conclude that the transfer of heat from a source with a low temperature to a source with a high temperature, as follows from the postulate of Clausius, necessarily requires energy (it cannot be performed by a free process without compensation).

A characteristic of the efficiency of refrigeration machines is the coefficient of performance

for the reverse Carnot cycle

The coefficient of performance of the reverse Carnot cycle depends on absolute temperatures and heat sources and has the highest value in comparison with the coefficient of performance of other cycles occurring within the same temperature range.

After considering the direct and reverse Carnot cycles, it is possible to explain in some detail the formulation of the second law of thermodynamics given by Clausius.

Clausius showed that all natural processes occurring in nature are spontaneous processes (they are sometimes called positive (or uncompensated processes) and cannot “by themselves” without compensation for the flow in the opposite direction.

Spontaneous processes include: the transfer of heat from a more heated body to a less heated one; the conversion of work into heat; mutual diffusion of liquids or gases; expansion of gas into a void, etc.

Non-spontaneous processes include processes that are opposite to the above spontaneous processes: the transfer of heat from a less heated body to a more heated one; converting heat into work; division into component parts of substances diffusing in each other, etc. Processes are not spontaneous, but they never proceed "by themselves" without compensation.

What processes must accompany non-spontaneous processes in order to make them possible? A careful and comprehensive study of the physical phenomena surrounding us has shown that non-spontaneous processes are only possible when they are accompanied by spontaneous processes. Consequently, a spontaneous process can occur "by itself", not spontaneous - only together with a spontaneous one. Therefore, for example, in any direct circular process, the non-spontaneous process of converting heat into work is compensated by the simultaneous spontaneous process of transferring part of the supplied heat from the heat sink to the heat sink. .

When implementing the reverse cycle, a non-spontaneous process of transferring heat from a less heated body to a more heated one is also possible, but here it is compensated by a spontaneous process of converting the work expended from outside into heat.

Thus, any non-spontaneous process can only occur when it is accompanied by a compensating spontaneous process.

Carnot's theorem

When deriving thermal efficiency. reversible Carnot cycle, relations were used that are valid only for an ideal gas. Therefore, in order to be able to extend everything said about the Carnot cycle to any real gases and vapors, it is necessary to prove that the thermal efficiency. Carnot cycle does not depend on the properties of the substance with which the cycle is carried out. This is the content of Carnot's theorem.

Heat. Work expended

The same result is obtained if we assume that . Therefore, one possible variant remains, when , which means that and , i.e., really thermal efficiency. reversible Carnot cycle does not depend on the properties of the working fluid and is only a function of the temperatures of the heat sink and heat sink.

Lecture No. 6. Subject and tasks of the theory of heat transfer

According to the second law of thermodynamics, a spontaneous process of heat transfer in space occurs under the influence of a temperature difference and is directed towards decreasing temperature. The laws of heat transfer and the quantitative characteristics of this process are the subject and task of studying the theory heat exchange (heat transfer).

The doctrine of heat transfer is the study of heat transfer processes. Their distinctive feature is their versatility, as they are of great importance in almost all branches of technology.

Thermal energy is transferred, like any other energy, in the direction from the highest potential to the lowest. Because the potential of thermal energy is the temperature, then the process of heat propagation is closely related to the temperature distribution, i.e., to the so-called temperature field. temperature field is the set of temperature values ​​in space and time. In general, the temperature t at any point in space is a function of the coordinates x, y, z and time τ and hence the temperature field equation will be

t = f(x, y, z, τ). (65)

A field in which the temperature changes with time is called transient, or non-stationary. If the temperature does not change with time, then the field is called steady state, or stationary, and its equation will be

t = f(x, y, z).(66)

The simplest case of a temperature field is a stationary one-dimensional field whose equation has the form

t = f(x). (67)

The heat transfer that occurs in a non-stationary temperature field is called heat transfer in non-stationary mode, and in a stationary field heat transfer in steady state.

The process of heat transfer is a complex process consisting of three elementary types of heat transfer - thermal conductivity, convection and thermal radiation (radiation) (Figure 12).

a - thermal conductivity; b - convection; a - radiation

Figure 12 - Varieties of heat transfer

Second law of thermodynamics- one of the basic laws of physics, the law of non-falling entropy in an isolated system. It places limits on the amount of useful work a heat engine can do. At a fundamental level, the second law of thermodynamics determines the direction of processes in a physical system - from order to disorder. There are many different formulations of the second law of thermodynamics, which are generally equivalent to each other.

1. Formulation

2. Alternative formulations

The above wording is very formal. There are many alternative formulations of the second law of thermodynamics. For example, Planck proposed this formulation:

It is impossible to build a machine that would cycle, cool a heat source or lift loads up without causing with no change in nature.

It is impossible to convert heat into work without performing any other action than cooling the system.

Nature tends to move from states with a lower probability of realization to states with a higher probability of realization.

It is impossible to create a perpetual motion machine of the 2nd kind

Spontaneous transfer of heat from less heated to more heated is impossible

Where there is a temperature difference, work can be done

The following expressions are common:

It is impossible to build a perpetual motion machine of the second kind.

It is impossible to transfer heat from a cold body to a hot one without expending energy.

Every system tends to move from order to disorder.

3. Historical background

The second law of thermodynamics was formulated in the middle of the 19th century, at the time when the theoretical basis for the design and construction of heat engines was being created. The experiments of Mayer and Joule established the equivalence between thermal and mechanical energies (the first law of thermodynamics). The question arose about the efficiency of heat engines. Experimental studies have shown that part of the heat is necessarily lost during the operation of any machine.

In the 1850s and 1860s, Clausius developed the concept of entropy in a number of publications. In 1865, he finally chose a name for the new concept. These publications also proved that heat cannot be completely converted into useful work, thus formulating the second law of thermodynamics.

Boltzmann gave a statistical interpretation to the second law of thermodynamics by introducing a new definition for entropy, which was based on microscopic atomistic concepts.

4. Statistical interpretation

From the statistical definition of entropy, it is obvious that the increase in entropy corresponds to the transition to such a macroscopic state, which is characterized by the highest value of microscopic states.

5. Arrow of time

If the initial state of a thermodynamic system is non-equilibrium, then over time it passes to an equilibrium state, increasing its entropy. This process proceeds only in one direction. The reverse process - the transition from the equilibrium state to the initial non-equilibrium state, is not realized. That is, the passage of time receives a direction.

The laws of physics that describe the microscopic world are invariant under the change of t to -t. This statement is true both for the laws of classical mechanics and the laws of quantum mechanics. In the microscopic world, conservative forces act, there is no friction, which is the dissipation of energy, i.e. the transformation of other types of energy into the energy of thermal motion, and this, in turn, is associated with the law of non-falling entropy.

Imagine, for example, a gas in a tank placed in a large tank. If you open the valve less than the reservoir, then after a while the gas will fill the larger reservoir in such a way that its density will even out. According to the laws of the microscopic world, there is also a reverse process, when gas from a larger reservoir is collected in a smaller reservoir. But in the macroscopic world, this never happens.

6. Heat death

If the entropy of each isolated system only increases with time, and the Universe is an isolated system, then someday the entropy will reach a maximum, after which any changes in it will become impossible.

Such reasoning, which appeared after the installation of the second law of thermodynamics, is called thermal death. This hypothesis was widely debated in the 19th century.

Every process in the world leads to the dissipation of part of the energy and its transformation into heat, to more and more disorder. Of course, our universe is still quite young. Thermonuclear processes in stars causing a constant flow of energy to the Earth, for example. The Earth is and will remain for a long time an open system that receives energy from various sources: from the Sun, from the processes of radioactive decay in the core, etc. In open systems, entropy can decrease, which leads to the appearance of various ordered structures.

A simple formulation of the first law of thermodynamics may sound something like this: a change in the internal energy of a system is possible only under external influence. That is, in other words, in order for some changes to occur in the system, it is necessary to make certain efforts from the outside. In folk wisdom, proverbs can serve as a kind of expression of the first law of thermodynamics - “water does not flow under a lying stone”, “you can’t easily pull a fish out of a pond” and so on. That is, using the proverb about fish and labor as an example, one can imagine that the fish is our conditionally closed system, no changes will occur in it (the fish will not pull itself out of the pond) without our external influence and participation (labor).

An interesting fact: it is the first law of thermodynamics that establishes why all the numerous attempts of scientists, researchers, inventors to invent a “perpetual motion machine” failed, because its existence is absolutely impossible according to this very law, why, see the paragraph above.

At the beginning of our article, there was a maximally simple definition of the first law of thermodynamics, in fact, in academic science there are as many as four formulations of the essence of this law:

• Energy does not appear from anywhere and does not disappear anywhere, it only passes from one form to another (the law of conservation of energy).
• The amount of heat received by the system is used to perform its work against external forces and change the internal energy.
• The change in the internal energy of a system during its transition from one state to another is equal to the sum of the work of external forces and the amount of heat transferred to the system, and does not depend on the method by which this transition is carried out.
• The change in the internal energy of a non-isolated thermodynamic system is equal to the difference between the amount of heat transferred to the system and the work done by the system on external forces.

Formula of the first law of thermodynamics

The formula for the first law of thermodynamics can be written as follows:

The amount of heat Q transferred to the system is equal to the sum of the change in its internal energy ΔU and the work A.

Processes of the first law of thermodynamics

Also, the first law of thermodynamics has its own nuances depending on the ongoing thermodynamic processes, which can be isochronous and isobaric, and below we will describe in detail about each of them.

First law of thermodynamics for an isochoric process

An isochoric process in thermodynamics is a process that occurs at a constant volume. That is, if you heat a substance in a vessel, whether in a gas or liquid, an isochoric process will occur, since the volume of the substance will remain unchanged. This condition also has an effect on the first law of thermodynamics, which takes place during an isochoric process.

In an isochoric process, the volume V is a constant, therefore, the gas does no work A = 0

From this comes the following formula:

Q = ΔU = U (T2) - U (T1).

Here U (T1) and U (T2) are the internal energies of the gas in the initial and final states. The internal energy of an ideal gas depends only on temperature (Joule's law). During isochoric heating, heat is absorbed by the gas (Q > 0), and its internal energy increases. During cooling, heat is transferred to external bodies (Q< 0).

First law of thermodynamics for isobaric process

Similarly, an isobaric process is a thermodynamic process that occurs in a system at a constant pressure and mass of gas. Therefore, in an isobaric process (p = const), the work done by the gas is expressed by the following equation of the first law of thermodynamics:

A = p (V2 - V1) = p ∆V.

The isobaric first law of thermodynamics gives:

Q \u003d U (T2) - U (T1) + p (V2 - V1) \u003d ΔU + p ΔV. With isobaric expansion, Q > 0, heat is absorbed by the gas, and the gas does positive work. Under isobaric compression Q< 0 – тепло отдается внешним телам. В этом случае A < 0. Температура газа при изобарном сжатии уменьшается, T2 < T1; внутренняя энергия убывает, ΔU < 0.

Application of the first law of thermodynamics

The first law of thermodynamics has a practical application to various processes in physics, for example, it allows you to calculate the ideal parameters of a gas in a variety of thermal and mechanical processes. In addition to a purely practical application, this law can also be used philosophically, because whatever you say, the first law of thermodynamics is an expression of one of the most general laws of nature - the law of conservation of energy. Even Ecclesiastes wrote that nothing appears from anywhere and does not go anywhere, everything stays forever, constantly transforming, and this is the whole essence of the first law of thermodynamics.

First law of thermodynamics video

And at the end of our article, your attention is an educational video about the first law of thermodynamics and internal energy.