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.

Heat absorbed (or released) during the isothermal expansion (or contraction) of one mole ideal gas, is equal to 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 algebraic sum of the reduced heats in the reversible Carnot cycle is equal to 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 closed circuit equals 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, but only changes right part equations, 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 wording: 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.

The second law of thermodynamics, like the first, is a postulate substantiated by the centuries-old experience of mankind. The discovery of this law was facilitated by the study of heat engines. French scientist S. Carnot first showed (1824) that any heat engine must contain, in addition to the source of heat (heater) and the working fluid (steam, ideal gas, etc.), which performs a thermodynamic cycle, also a refrigerator, which has a temperature necessarily lower than the temperature of the heater.

Efficiency η such a heat engine operating on a reversible cycle ( Carnot cycle), does not depend on the nature of the working fluid that performs this cycle, but is determined only by the temperatures of the heater T 1 and refrigerator T 2:

where Q 1 - the amount of heat communicated to the working fluid at a temperature T 1 from the heater; Q 2 - the amount of heat given off by the working fluid at a temperature T 2 fridge.

The second law of thermodynamics is a generalization of Carnot's conclusion to arbitrary thermodynamic processes occurring in nature. Several formulations of this law are known.

Clausius(1850) formulated second law of thermodynamics So: no process is possible in which heat would transfer spontaneously from colder bodies to hotter bodies.

W. Thomson (Kelvin)(1851) proposed the following formulation: it is impossible to build a periodically operating machine, the entire activity of which would be reduced to making mechanical work and appropriate tank cooling.

Thomson's postulate can be formulated as follows: a perpetual motion machine of the second kind is impossible. A perpetual motion machine of the second kind is a device that, without compensation, would periodically completely convert the heat of a body into work (W. Ostwald). Under compensation understand the change in the state of the working fluid or the transfer of part of the heat by the working fluid to other bodies and the change in the thermodynamic state of these bodies during the circular process of converting heat into work.

The second law of thermodynamics states that without compensation in a circular process, not a single joule of heat can be converted into work. Work is converted into heat completely without any compensation.. The latter is connected, as noted earlier, with the spontaneity of the process of dissipation (depreciation) of energy.

The second law of thermodynamics introduces a system state function that quantitatively characterizes the process of energy dissipation. In this sense, the above formulations of the second law of thermodynamics are equivalent, since they imply the existence functions of the state of the system - entropy.

Currently second law of thermodynamics is formulated as follows: there is an additive function of the state of the system S - entropy, which is related to the heat entering the system and the temperature of the system in the following way:

For reversible processes; (3.2)

For irreversible processes. (3.3)

In this way, in reversible processes in an adiabatically isolated system, its entropy does not change (dS = 0), and in irreversible processes increases (dS > 0).

Unlike internal energy, the value of the entropy of an isolated system depends on the nature of the processes occurring in it: in the course of relaxation, the entropy of an isolated system should increase, reaching gaya maximum value at equilibrium.

AT general view second law of thermodynamics for an isolated system is written like this:

The entropy of an isolated system either increases if spontaneous irreversible processes take place in it, or remains constant. Therefore, the second law of thermodynamics is also defined as the law of non-decreasing entropy in isolated systems.

So the second law of thermodynamics gives criterion for the spontaneity of processes in an isolated system. Only processes accompanied by an increase in entropy can occur spontaneously in such a system. Spontaneous processes end with the establishment of equilibrium in the system. Hence, in the state of equilibrium, the entropy of an isolated system is maximum. According to this equilibrium criterion in an isolated system will be

If the process involves non-isolated system, then to assess the irreversibility (spontaneity) of the process, it is necessary to know the change in the entropy of the system dS 1 and entropy change environment dS 2. If we accept that system and environment(often referred to as the "universe") form an isolated system, then the condition for the irreversibility of the process will be

that is the process will be irreversible if the total change in the entropy of the system and the environment is greater than zero.

The environment is a huge reservoir; its volume and temperature do not change during heat exchange with the system. Therefore, for the environment it is possible to equate δQ = dU and it does not matter whether the heat transfer occurs reversibly or irreversibly, since δQ arr, and δQ not exactly equal dU environment. In this way, the change in the entropy of the environment is always equal to.

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 theoretical background for the design and construction of thermal engines. 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, characterized by highest value microscopic conditions.

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 laws classical mechanics, and laws 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 processes radioactive decay in the core etc. In open systems, the entropy can decrease, which leads to the appearance of various ordered structures.

Entropy. Second law of thermodynamics

spontaneous processes. In nature, physical and chemical transformations take place in a certain direction. So, two bodies at different temperatures come into contact, thermal energy is transferred from a warmer body to a colder one until the temperature of these two bodies is equal. When a zinc plate is immersed in hydrochloric acid, ZnCl 2 and H2. All these transformations are spontaneous (spontaneous)). A spontaneous process cannot take place in reverse direction just as spontaneously as in a direct one.

In chemistry, it is important to know the criteria to foresee whether chemical reaction occur spontaneously, and if possible, be able to determine the amount of products formed. The first law of thermodynamics does not provide such a criterion. The thermal effect of the reaction does not determine the direction of the process. Both exothermic and endothermic reactions can spontaneously occur. So, for example, the process of dissolving ammonium nitrate spontaneously takes place NH 4 NO 3 (to) in water, although the thermal effect of this process is positive: > 0 (endothermic process); the same can be said about the dissolution of sodium hyposulfite in water. And in another example, it is impossible to implement when T = 298 K and p = 101 kPa (1 atm) synthesis n. heptane C 7 H 16 (w), despite the fact that the standard heat of its formation is negative:< 0 (процесс экзотермический).

Thus, the difference in the enthalpies of the reaction does not yet determine the possibility of its occurrence under given specific conditions.

The second law of thermodynamics. The criterion for the spontaneous flow of a process in isolated systems gives the second law of thermodynamics.

The second law of thermodynamics makes it possible to divide all processes allowed by the first law into spontaneous and non-spontaneous.

The second law of thermodynamics is postulate substantiated by the great experience accumulated by mankind. It is expressed in different equivalent formulations:

1. Heat cannot transfer by itself from a less heated body to a more heated one - the postulate of Clausius (1850). It is argued that the process of heat conduction is irreversible.

2. Quickly or slowly, any system tends to a state of true equilibrium.

3. A periodic process is impossible, the only result of which is the conversion of heat into work - the formulation of Kelvin - Planck.

4. Heat can go into work only in the presence of a temperature difference and not entirely, but with a certain thermal efficiency:

where η - thermal efficiency; A is the work received by the system due to the transfer of heat from a body with a high temperature ( T1) to a body with a low temperature ( T2); Q1 is the heat taken from a body heated with a temperature T1; Q2 is the heat given to a cold body with a temperature T2. Those. any processes proceed under the action of a potential difference, which for thermal processes is the temperature difference, for electrical processes it is the potential difference, for mechanical processes it is the height difference, etc. A common feature is a relatively low efficiency. The efficiency value turns to unity if T2 → 0, but absolute zero is unattainable (the third law of thermodynamics), therefore, all the energy of a heated body at T1 cannot be turned into work. Those. when work is done, part of the total energy of the system remains unused.

The concept of entropy. Exploring the expression for efficiency heat engine Clausius introduced a new thermodynamic function, which he called entropy - S.

The operation of an ideal heat engine (Carnot cycle) is discussed in detail in the physics course.

From the mathematical expression of the second law of thermodynamics it follows:

or

AT differential form:

Summing up the changes over the entire cycle of the heat engine, we obtain the expression where dQ- increase in heat T is the corresponding temperature; is a closed loop integral.

Clausius took the integrand expression as the increment of the new function S- entropy:

or

Entropy is a function of system state parameters (p, V, T) and can evaluate the direction of the process in a system tending to equilibrium, since for an equilibrium process, its change is zero; or .

In the case of an irreversible transformation, i.e. spontaneous process proceeding at a constant temperature, we have

If the process proceeds spontaneously, then the change in entropy is positive:

For isolated systems, processes for which the change in entropy < 0 are prohibited.

If the universe is chosen as an isolated system, then the second law of thermodynamics can be formulated as follows:

There is a function S called entropy, which is a state function such that

In the case of a reversible process, the entropy of the universe is constant, and in the case of an irreversible process it increases. The entropy of the universe cannot decrease.”

Statistical interpretation of entropy. To characterize the state of a certain mass of matter, which is a collection of a very large number of molecules, one can indicate the parameters of the state of the system and thus characterize the macrostate of the system; but you can specify the instantaneous coordinates of each molecule (x i , y i , z i) and speed of movement in all three directions Vx i , Vy i , Vz i, i.e. characterize the microstate of the system. Each macrostate corresponds to a huge number of microstates. The number of microstates corresponding to the macroscopic state is determined by the exact values ​​of the state parameters and is denoted by W is the thermodynamic probability of the state of the system.

The thermodynamic probability of the state of a system consisting of only 10 gas molecules is approximately 1000, and in fact only 1 cm 3 of gas contains 2.7 ∙ 10 19 molecules (n.o.). Therefore, thermodynamics does not use the quantity W, and its logarithm lnW. The latter can be given the dimension (J/K), multiplying by the Boltzmann constant To:

W, where \u003d 1.38 10 -23 J / K,

where N A- Avogadro's number

the value S called entropy systems. Entropy is a thermodynamic function of the state of a system.

If an isolated system is in a macroscopic state 1 corresponding W 1 microscopic states and if it can go into a macroscopic state 2 , the number of microscopic states of which W2, then the system will tend to go into the state 2 provided that W2 > W1

The system spontaneously tends to the state that, on a microscopic scale, corresponds to the largest number of implementation possibilities.

For example, when an ideal gas expands into a vacuum, the final state (with a larger volume than the initial state) includes a much larger number of microstates, simply because the molecules can take on a greater number of positions in space.

When a spontaneous process occurs in an isolated system, the number of microscopic states W increases; The same can be said about the entropy of the system. As the number of microscopic states increases W associated with the macroscopic state of the system, the entropy increases.

For example, consider the thermodynamic state of 1 mole of water ( 18 g H2O) under standard conditions. Let W (w) is the thermodynamic probability of the state of this system. When the temperature drops to 0 ºС water freezes, turns into ice; while the water molecules seem to be fixed in the nodes crystal lattice and the thermodynamic probability of the state of the system decreases; W(k)< W (ж). Therefore, the entropy of the system also decreases: (to)< (ж). Conversely, as the temperature rises to 100º C water boils and turns into steam; in this case, the thermodynamic probability of the state of the system increases: W (d) > W (w), therefore, the entropy of the system also increases:

(d) > (g).

Entropy is thus a measure of the disorder in the state of a system. Indeed, the only microscopic state ( W=1) will correspond to complete ordering and zero entropy, i.e. the position, speed, energy of each particle are known, and all these microscopic characteristics will remain constant in time.

The second law of thermodynamics can be formulated as follows:

An isolated system tends to reach the most probable state, i.e. macroscopic state corresponding the largest number microscopic conditions.

In isolated systems, only those processes occur spontaneously that are accompanied by an increase in the entropy of the system: ΔS > 0 (ΔS \u003d S 2 - S 1).

The entropy of pure substances that exist in the form of ideal crystals at a temperature of absolute zero is zero. This means that at absolute zero, complete order is achieved.

irreversible called physical process, which can spontaneously flow in only one specific direction.

In the opposite direction, such processes can proceed only as one of the links in a more complex process.

Almost all processes occurring in nature are irreversible. This is due to the fact that in any real process, part of the energy is dissipated due to radiation, friction, etc. For example, heat, as you know, always passes from a hotter body to a colder one - this is the most typical example of an irreversible process does not violate the law of conservation of energy).

Also, a ball (pendulum) hanging on a light thread will never spontaneously increase the amplitude of its oscillations, on the contrary, once set in motion by an outside force, it will eventually stop as a result of air resistance and friction of the thread against the suspension. Thus, reported to the pendulum mechanical energy goes into internal energy chaotic movement of molecules (air, suspension material).

Mathematically, the irreversibility of mechanical processes is expressed in the fact that the equation of motion of macroscopic bodies changes with a change in the sign of time: they are not invariant when replacing t on the - t. In this case, acceleration and forces that depend on distances do not change their signs. Sign when replacing t on the - t changes with speed. Accordingly, the sign changes the force depending on the speed - the friction force. That is why, when work is done by friction forces, the kinetic energy of the body is irreversibly converted into internal energy.

The direction of processes in nature indicates second law of thermodynamics.

The second law of thermodynamics.

Second law of thermodynamics- one of the basic laws of thermodynamics, establishing the irreversibility of real thermodynamic processes.

The second law of thermodynamics was formulated as a law of nature by N. L. S. Carnot in 1824, then by W. Thomson (Kelvin) in 1841 and R. Clausius in 1850. The formulations of the law are different, but equivalent.

The German scientist R. Clausius formulated the law as follows: it is impossible to transfer heat from a colder system to a hotter one in the absence of other simultaneous changes in both systems or surrounding bodies. This means that heat cannot spontaneously move from a colder body to a hotter one ( Clausius principle).

According to Thomson's formulation, the process in which work is converted into heat without any other changes in the state of the system is irreversible, i.e. it is impossible to convert all the heat taken from the body into work without making any other changes in the state of the system ( Thomson principle).