There are several formulations of the second law of thermodynamics, two of which are given below:

· heat cannot by itself move from a body with a lower temperature to a body with a higher temperature(formulation by R. Clausius);

· a perpetual motion machine of the second kind is impossible, that is, such a periodic process, the only result of which would be the conversion of heat into work due to the cooling of one body (Thomson’s formulation).

The second law of thermodynamics indicates the inequality of two forms of energy transfer - work and heat. This law takes into account the fact that the process of transition of the energy of ordered motion of a body as a whole (mechanical energy) into the energy of disordered motion of its particles (thermal energy) is irreversible. For example, mechanical energy during friction is converted into heat without any additional processes. The transition of the energy of disordered particle motion (internal energy) into work is possible only if it is accompanied by some additional process. Thus, a heat engine operating in a direct cycle produces work only due to the heat supplied from the heater, but at the same time part of the received heat is transferred to the refrigerator.

Entropy. In addition to internal energy U, which is a unique function of the state parameters of the system; other state functions are widely used in thermodynamics ( free energy, enthalpy And entropy).

Concept entropy introduced in 1865 by Rudolf Clausius. This word comes from the Greek. entropia and literally means turn, transformation. in thermodynamics, this term is used to describe the transformation of various types of energy (mechanical, electrical, light, chemical) into heat, that is, into the random, chaotic movement of molecules. It is impossible to collect this energy and transform it back into the species from which it was obtained.

For determining measures of irreversible scattering or dissipation energy and this concept was introduced. Entropy S is a function of state. It stands out among other thermodynamic functions in that it has statistical, that is, probabilistic nature.

If a process involving the receipt or release of heat occurs in a thermodynamic system, this leads to a transformation of the entropy of the system, which can either increase or decrease. During an irreversible cycle, the entropy of an isolated system increases

dS> 0. (3.4)

This means that irreversible energy dissipation occurs in the system.

If a reversible process occurs in a closed system, the entropy remains unchanged

dS= 0. (3.5)

The change in entropy of an isolated system to which an infinitesimal amount of heat is imparted is determined by the relation:

. (3.6)

This relationship is valid for a reversible process. For an irreversible process occurring in a closed system, we have:

dS> .

In an open system, entropy always increases. The state function whose differential is is called reduced heat.

Thus, in all processes occurring in a closed system, entropy increases during irreversible processes and remains unchanged during reversible processes. Consequently, formulas (3.4) and (3.5) can be combined and presented in the form

dS ³ 0.

This statistical formulation of the second law of thermodynamics.

If the system makes an equilibrium transition from state 1 to state 2, then according to equation (3.6) , entropy change

D S 1- 2 = S 2 – S 1 = .

It is not entropy itself that has a physical meaning, but the difference between entropies.

Let's find the change in entropy in ideal gas processes. Because the:

; ;

,

or: . (3.7)

This shows that the change in the entropy of an ideal gas during the transition from state 1 to state 2 does not depend on the type of transition process 1® 2.

From formula (3.7) it follows that when isothermal process ( T 1 = T 2):

.

At isochoric process, the change in entropy is equal to

.

Since for an adiabatic process d Q= 0, then uD S= 0, therefore, a reversible adiabatic process occurs at constant entropy. That's why they call him isentropic process.

The entropy of a system has the property of additivity, which means that the entropy of the system is equal to the sum of the entropies of all bodies that are included in the system.

The meaning of entropy becomes clearer if we involve statistical physics. In it, entropy is associated with thermodynamic probability of the system state. The thermodynamic probability W of the state of the system is equal to the number of all possible microdistributions of particles along coordinates and velocities, which determines a given macrostate: Walways³ 1, that is thermodynamic probability is not probability in the mathematical sense.

L. Boltzmann (1872) showed that the entropy of a system is equal to the product of Boltzmann's constant k by the logarithm of the thermodynamic probability W of a given state

Consequently, entropy can be given the following statistical interpretation: entropy is a measure of the disorder of a system. From formula (3.8) it is clear: the greater the number of microstates that realize a given macrostate, the greater the entropy. The most probable state of the system is an equilibrium state. The number of microstates is maximum, therefore, entropy is maximum.

Since all real processes are irreversible, it can be argued that all processes in a closed system lead to an increase in entropy - the principle of increasing entropy.

In the statistical interpretation of entropy, this means that processes in a closed system proceed in the direction from less probable states to more probable states until the probability of states becomes maximum.

Let's explain with an example. Let's imagine a vessel divided by a partition into two equal parts A And B. In part A there is gas, and in B- vacuum. If you make a hole in the partition, the gas will immediately begin to expand “by itself” and after some time will be evenly distributed throughout the entire volume of the vessel, and this will most likely state of the system. Least likely there will be a state when most of the gas molecules suddenly spontaneously fill one of the halves of the vessel. You can wait for this phenomenon as long as you like, but the gas itself will not reassemble into parts. A. To do this, you need to do some work on the gas: for example, move the right wall of a part like a piston B. Thus, any physical system tends to move from a less probable state to a more probable state. The equilibrium state of the system is more probable.

Using the concept of entropy and R. Clausius’ inequality, second law of thermodynamics can be formulated as the law of increasing entropy of a closed system during irreversible processes:

any irreversible process in a closed system occurs in such a way that the system is more likely to enter a state with higher entropy, reaching a maximum in a state of equilibrium. Or else:

in processes occurring in closed systems, entropy does not decrease.

Please note that we are talking only about closed systems.

So, the second law of thermodynamics is a statistical law. It expresses the necessary patterns of chaotic motion of a large number of particles that are part of an isolated system. However, statistical methods are applicable only in the case of a huge number of particles in the system. For a small number of particles (5-10) this approach is not applicable. In this case, the probability of all particles being in one half of the volume is no longer zero, or in other words, such an event can occur.

Heat Death of the Universe. R. Clausius, considering the Universe as a closed system, and applying the second law of thermodynamics to it, reduced everything to the statement that the entropy of the Universe must reach its maximum. This means that all forms of motion must turn into thermal motion, as a result of which the temperature of all bodies in the Universe will become equal over time, complete thermal equilibrium will occur, and all processes will simply stop: the thermal death of the Universe will occur.

Basic equation of thermodynamics . This equation combines the formulas of the first and second laws of thermodynamics:

d Q = dU + p dV, (3.9)

Let us substitute equation (3.9), expressing the second law of thermodynamics, into equality (3.10):

.

That's what it is fundamental equation of thermodynamics.

In conclusion, we note once again that if the first law of thermodynamics contains the energy balance of the process, then the second law shows its possible direction.

Third law of thermodynamics

Another law of thermodynamics was established in the process of studying changes in the entropy of chemical reactions in 1906 by V. Nernst. It's called Nernst's theorem or third law of thermodynamics and is associated with the behavior of the heat capacity of substances at absolute zero temperatures.

Nernst's theorem states that when approaching absolute zero, the entropy of the system also tends to zero, regardless of what values ​​all other parameters of the system’s state take:

.

Since entropy , and the temperature T tends to zero, the heat capacity of the substance must also tend to zero, and faster than T. this implies unattainability of absolute zero temperature with a finite sequence of thermodynamic processes, that is, a finite number of operations - operating cycles of the refrigeration machine (the second formulation of the third law of thermodynamics).

Real gases

Van der Waals equation

The change in the state of rarefied gases at sufficiently high temperatures and low pressures is described by the ideal gas laws. However, as the pressure increases and the temperature of a real gas decreases, significant deviations from these laws are observed, due to significant differences between the behavior of real gases and the behavior that is attributed to particles of an ideal gas.

The equation of state of real gases must take into account:

· final value of the molecules’ own volume;

· mutual attraction of molecules to each other.

For this, J. van der Waals proposed to include in the equation of state not the volume of the vessel, as in the Clapeyron-Mendeleev equation ( pV = RT), and the volume of a mole of gas not occupied by molecules, that is, the value ( V m -b), Where V m – molar volume. To take into account the forces of attraction between molecules, J. van der Waals introduced a correction to the pressure included in the equation of state.

By introducing corrections related to taking into account the intrinsic volume of molecules (repulsive forces) and attractive forces into the Clapeyron-Mendeleev equation, we obtain equation of state of a mole of real gas as:

.

This van der Waals equation, in which the constants A And b have different meanings for different gases.

Laboratory work

Second law of thermodynamics(second law of thermodynamics) establishes the existence of entropy as a function of the state of a thermodynamic system and introduces the concept of absolute thermodynamic temperature, that is, “the second law is the law of entropy” and its properties. In an isolated system, entropy remains either constant or increases (in nonequilibrium processes), reaching a maximum when thermodynamic equilibrium is reached ( law of increasing entropy) . Various formulations of the second law of thermodynamics found in the literature are particular expressions of the general law of increasing entropy.

The second law of thermodynamics allows us to construct a rational temperature scale that does not depend on arbitrariness in the choice of a thermometric property and the method of measuring it.

Together, the first and second principles form the basis of phenomenological thermodynamics, which can be considered as a developed system of consequences of these two principles. At the same time, of all the processes allowed by the first law in a thermodynamic system, the second law allows us to identify the actually possible ones and establish the direction of spontaneous processes, as well as the criteria for equilibrium in thermodynamic systems

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The second law of thermodynamics arose as a working theory of heat engines, which establishes the conditions under which the conversion of heat into work achieves maximum effect. Analysis of the second law of thermodynamics shows that the small magnitude of this effect ─ coefficient of performance (efficiency) ─ is determined not by the technical imperfection of heat engines, but by the peculiarity of heat as a method of energy transfer, which imposes restrictions on its value. The first theoretical studies of the operation of heat engines were carried out by the French engineer Sadi Carnot. He came to the conclusion that the efficiency of heat engines does not depend on the thermodynamic cycle and the nature of the working fluid, but is entirely determined depending on external sources - the heater and refrigerator. Carnot's work was written before the discovery of the principle of equivalence of heat and work and the general recognition of the law of conservation of energy. Carnot based his conclusions on two contradictory grounds: the caloric theory, which was soon discarded, and hydraulic analogy. Somewhat later, R. Clausius and W. Thomson-Kelvin reconciled Carnot’s theorem with the law of conservation of energy and laid the foundation for what now constitutes the content of the second law of thermodynamics.

To substantiate Carnot's theorem and further construct the second law, it was necessary to introduce a new postulate.

The most common formulations of the postulate of the second law of thermodynamics

Postulate of Clausius (1850):

Heat cannot transfer spontaneously from a colder body to a warmer one..

Thomson-Kelvin postulate (1852) as formulated by M. Planck:

It is impossible to build a periodically operating machine, all of whose activity is reduced to lifting weights and cooling the thermal reservoir.

An indication of the frequency of operation of the machine is essential, since it is possible non-circular process, the only result of which would be the production of work due to the internal energy received from the thermal reservoir. This process does not contradict the Thomson-Kelvin postulate, since the process is non-circular and, therefore, the machine is not periodically operating. Essentially, Thomson's postulate speaks of the impossibility of creating a perpetual motion machine of the second kind, which is capable of continuously doing work by taking heat from an inexhaustible source. In other words, it is impossible to realize a heat engine whose only result would be the conversion of heat into work without compensation, that is, without some of the heat being transferred to other bodies and thus irretrievably lost to obtain work.

It is easy to prove that the postulates of Clausius and Thomson are equivalent. The proof comes from the opposite.

Let us assume that the Clausius postulate is not satisfied. Let us consider a heat engine, the working substance of which received an amount of heat from a hot source during a cycle Q 1 (\displaystyle Q_(1)), gave an amount of heat to the cold source and performed work. Since, by assumption, the Clausius postulate is not true, it is possible to warmly Q 2 (\displaystyle Q_(2)) return to the hot spring without changing the environment. As a result, the state of the cold source did not change, the hot source gave the amount of heat to the working substance Q 2 − Q 1 (\displaystyle Q_(2)-Q_(1)) and due to this heat the machine did the work A = Q 1 − Q 2 (\displaystyle A=Q_(1)-Q_(2)), which contradicts Thomson's postulate.

The postulates of Clausius and Thomson-Kelvin are formulated as a denial of the possibility of any phenomenon, i.e. as postulates of prohibition. The postulates of the prohibition do not at all correspond to the content and modern requirements for substantiating the principle of the existence of entropy and do not fully satisfy the task of substantiating the principle of increasing entropy, since they must contain an indication of a certain direction of irreversible phenomena observed in nature, and not deny the possibility of their opposite course.

• Planck's postulate (1926):

The generation of heat by friction is irreversible.

Planck's postulate, along with the denial of the possibility of complete conversion of heat into work, contains a statement about the possibility of complete conversion of work into heat.

Modern formulation of the second law of classical thermodynamics.

The second law of thermodynamics is a statement about the existence of a certain state function ─ entropy in any equilibrium system and its non-decrease during any processes in isolated and adiabatically isolated systems.

In other words, the second law of thermodynamics is combined principle of existence and increase of entropy.

The principle of the existence of entropy is a statement of the second law of classical thermodynamics about the existence of a certain function of the state of bodies (thermodynamic systems) ─ entropy S (\displaystyle S), the differential of which is a total differential d S (\displaystyle dS), and is defined in reversible processes as the ratio of the elementary amount of heat supplied from outside δ Q arr ∗ (\displaystyle \delta Q_(\text(arr))^(*)) to the absolute temperature of the body (system) T (\displaystyle T):

D S arr = δ Q arr ∗ T (\displaystyle dS_(\text(arr))=(\frac (\delta Q_(\text(arr))^(*))(T)))

The principle of increasing entropy is a statement of the second law of classical thermodynamics about the constant increase in the entropy of isolated systems in all real processes of change in their state. (In reversible processes of changing the state of isolated systems, their entropy does not change).

D S insulated ≥ 0 (\displaystyle dS_(\text(isolated))\geq 0)

Mathematical expression of the second law of classical thermodynamics:

D S = δ Q ∗ T ≥ 0 (\displaystyle dS=(\frac (\delta Q^(*))(T))\geq 0)

Statistical definition of entropy

In statistical physics, entropy (S) (\displaystyle (S)) thermodynamic system is considered as a function of probability (W) (\displaystyle (W)) its state (“Boltzmann principle”).

S = k l n W , (\displaystyle S=klnW,)

Where k (\displaystyle k)─ Boltzmann constant, W (\displaystyle W)─ thermodynamic probability of a state, which is determined by the number of microstates realizing a given macrostate.

Methods for substantiating the second law of thermodynamics.

R. Clausius method

In his substantiation of the second law, Clausius examines the circular processes of two mechanically coupled reversible heat engines using an ideal gas as a working fluid, proves Carnot's theorem (an expression for the efficiency of a reversible Carnot cycle) for ideal gases η = 1 − T 2 T 1 (\displaystyle \eta =1-(\frac (T_(2))(T_(1)))), and then states a theorem called the Clausius integral:

∮ ⁡ δ Q T = 0 (\displaystyle \oint (\frac (\delta Q)(T))=0)

From the equality to zero of the circular integral it follows that its integrand is the total differential of some state function ─ S (\displaystyle S), and the following equality is a mathematical expression of the principle of the existence of entropy for reversible processes:

D S = δ Q T (\displaystyle dS=(\frac (\delta Q)(T)))

Next, Clausius proves the inequality of the efficiency of reversible and irreversible machines and, ultimately, comes to the conclusion that the entropy of isolated systems does not decrease: Many objections and comments were expressed regarding the construction of the second law of thermodynamics using the Clausius method. Here are some of them:

1. Clausius begins the construction of the principle of the existence of entropy by expressing the efficiency of a reversible Carnot cycle for ideal gases, and then extends it to all reversible cycles. Thus, Clausius implicitly postulates the possibility of the existence of ideal gases that obey the Clapeyron equation P v = R T (\displaystyle Pv=RT) and Joule's law u = u (t) (\displaystyle u=u(t)) .

2. The justification of Carnot's theorem is erroneous, since an extra condition is introduced into the proof scheme - a more advanced reversible machine is invariably assigned the role of a heat engine. However, if we accept that a refrigeration machine is a more perfect machine, and instead of Clausius’s postulate we accept the opposite statement that heat cannot spontaneously transfer from a hotter body to a colder one, then Carnot’s theorem will also be proven in the same way. Thus, the conclusion suggests itself that the principle of the existence of entropy does not depend on the direction of spontaneous processes, and the postulate of irreversibility cannot be the basis for proving the existence of entropy.

3. The Clausius postulate as a prohibition postulate is not an explicit statement characterizing the direction of occurrence of irreversible phenomena observed in nature, in particular, a statement about the spontaneous transition of heat from a hotter body to a colder one, since the expression ─ can't cross is not equivalent to the expression goes over.

4. Conclusions of statistical physics about the probabilistic nature of the principle of irreversibility and the discovery in 1951 unusual (quantum) systems with negative absolute temperatures, in which spontaneous heat transfer has the opposite direction, heat can be completely converted into work, and work cannot be completely (without compensation) converted into heat, the basic postulates of Clausius, Thomson-Kelvin and Planck were shaken, completely rejecting some and imposing serious restrictions on others.

Schiller–Carathéodory method

In the 20th century, thanks to the works of N. Schiller, C. Carathéodory, T. Afanasyeva - Ehrenfest, A. Gukhman and N.I. Belokon, a new axiomatic direction appeared in the substantiation of the second law of thermodynamics. It turned out that the principle of the existence of entropy can be substantiated regardless of the direction of real processes observed in nature, i.e. from the principle of irreversibility, and to determine absolute temperature and entropy it is not required, as Helmholtz noted, either to consider circular processes or to assume the existence of ideal gases. In 1909, Constantin Carathéodory, a prominent German mathematician, published a work in which he substantiated the principle of the existence of entropy not as a result of studying the states of real thermodynamic systems, but on the basis of a mathematical consideration of expressions for reversible heat transfer as differential polynomials (Pfaff forms). Even earlier, at the turn of the century, N. Schiller came to similar constructions, but his works went unnoticed until T. Afanasyeva-Ehrenfest drew attention to them in 1928.

Carathéodory's postulate (postulate of adiabatic unattainability).

Near each equilibrium state of the system, such states are possible that cannot be achieved using a reversible adiabatic process.

Carathéodory's theorem states that if the Pfaff differential polynomial has the property that in an arbitrary vicinity of a certain point there are other points that are unreachable by successive movements along the path, then there are integrating divisors of this polynomial and the equation ∑ X i d x i = 0 (\displaystyle \sum X_(i)dx_(i)=0).

M. Planck was critical of Carathéodory's method. Carathéodory’s postulate, in his opinion, is not one of the visual and obvious axioms: “The statement contained in it is not generally applicable to natural processes... . No one has ever carried out experiments with the goal of achieving all adjacent states of any specific state in an adiabatic way.” Planck contrasts the Carathéodory system with his own system based on the postulate: “The formation of heat through friction is irreversible,” which, in his opinion, exhausts the content of the second law of thermodynamics. The Carathéodory method, meanwhile, was highly praised in the work of T. Afanasyeva-Ehrenfest “Irreversibility, one-sidedness and the second law of thermodynamics” (1928). In her remarkable article, Afanasyeva-Ehrenfest came to a number of important conclusions, in particular:

1. The main content of the second law is that the elementary amount of heat δ Q (\displaystyle \delta Q), which the system exchanges in a quasistic process, can be represented in the form T d S (\displaystyle TdS), Where T = f (t) (\displaystyle T=f(t))─ a universal function of temperature, called absolute temperature, and (S) (\displaystyle (S))─ function of system state parameters, called entropy. Obviously the expression δ Q = T d S (\displaystyle \delta Q=TdS) has the meaning principle of the existence of entropy.

2. The fundamental difference between nonequilibrium processes and equilibrium ones is that under conditions of inhomogeneity of the temperature field, a transition of the system to a state with a different entropy is possible without heat exchange with the environment. (This process was later called “internal heat exchange” or heat exchange of the working fluid in the works of N.I. Belokon.) The consequence of the non-equilibrium process in an isolated system is its one-sidedness.

3. A one-sided change in entropy is equally conceivable as its steady increase or its steady decrease. Physical prerequisites, such as adiabatic unattainability and irreversibility of real processes, do not express any requirements regarding the preferential direction of the flow of spontaneous processes.

4. To reconcile the obtained conclusions with experimental data for real processes, it is necessary to accept a postulate, the scope of which is determined by the limits of applicability of these data. This postulate is the principle entropy increase.

A. Gukhman, assessing Carathéodory’s work, believes that it “is distinguished by formal logical rigor and impeccability in mathematical terms... At the same time, in the pursuit of the greatest generality, Carathéodory gave his system such an abstract and complex form that it turned out to be virtually inaccessible to the majority physicists of that time." Regarding the postulate of adiabatic unattainability, Gukhman notes that as a physical principle it cannot be the basis of a theory of universal significance, since it does not have the property of self-evidence. “Everything is extremely clear in relation to a simple...system...But this clarity is completely lost in the general case of a heterogeneous system, complicated by chemical transformations and exposed to external fields.” He also talks about how right Afanasyeva-Ehrenfest was in insisting on the need to completely separate the problem of the existence of entropy from everything connected with the idea of ​​​​the irreversibility of real processes.” Regarding the construction of the foundations of thermodynamics, Gukhman believes that “there is no independent separate problem of the existence of entropy. The question comes down to extending to the case of thermal interaction a range of concepts developed on the basis of the experience of studying all other energy interactions, and culminating in the establishment of a uniform equation for the elementary amount of influence d Q = P d x (\displaystyle dQ=Pdx) This extrapolation is suggested by the very structure of ideas. Undoubtedly, there are sufficient grounds to accept it as a very plausible hypothesis and thereby postulate the existence of entropy.

N.I. Belokon, in his monograph “Thermodynamics”, gave a detailed analysis of numerous attempts to substantiate the second law of thermodynamics as a unified principle of the existence and increase of entropy based only on the postulate of irreversibility. He showed that attempts at such justification do not correspond to the modern level of development of thermodynamics and cannot be justified, firstly, because the conclusion about the existence of entropy and absolute temperature has nothing to do with the irreversibility of natural phenomena (these functions exist regardless of increase or decrease entropy of isolated systems), secondly, an indication of the direction of observed irreversible phenomena reduces the level of generality of the second law of thermodynamics and, thirdly, the use of the Thomson-Planck postulate about the impossibility of completely converting heat into work contradicts the results of studies of systems with negative absolute temperature, in which complete conversion of heat into work can be accomplished, but complete conversion of work into heat is impossible. Following T. Afanasyeva-Ehrenfest N.I. Belokon argues that the difference in content, level of generality and scope of application of the principles of the existence and increase of entropy is quite obvious:

1. From the principle of the existence of entropy a number of the most important differential equations thermodynamics, widely used in the study of thermodynamic processes and physical properties of matter, and its scientific significance cannot be overestimated.

2. The principle of increasing entropy of isolated systems is a statement about the irreversible flow of phenomena observed in nature. This principle is used in judgments about the most likely direction of the flow of physical processes and chemical reactions, and everything follows from it. inequalities thermodynamics.

Regarding the substantiation of the principle of the existence of entropy using the Schiller ─ Carathéodory method, Belokon notes that in constructing the principle of existence using this method, it is absolutely necessary to use Carathéodory’s theorem on the conditions for the existence of integrating divisors of differential polynomials δ Q = ∑ X i d x i = τ d Z , (\displaystyle \delta Q=\sum X_(i)dx_(i)=\tau dZ,) however, the need to use this theorem “should be considered very constraining, since the general theory of differential polynomials of the type under consideration (Pfaffian forms) presents certain difficulties and is presented only in special works on higher mathematics.” In most thermodynamics courses, Carathéodory's theorem is given without proof, or the proof is given in a non-rigorous, simplified form. .

Analyzing the construction of the principle of existence of entropy of equilibrium systems according to the scheme of C. Carathéodory, N.I. Belokon draws attention to the use of a completely unfounded assumption about the possibility of simultaneously turning on the temperature t (\displaystyle t) and ─ functions into the independent variables of the state of the equilibrium system and comes to the conclusion that that Carathéodory's postulate is equivalent to the group of general conditions for the existence of integrating divisors of differential polynomials ∑ X i d x i (\displaystyle \sum X_(i)dx_(i)), But insufficient to establish the existence primary integrating divisor τ (t) = T (\displaystyle \tau (t)=T), i.e. to justify the principle of the existence of absolute temperature and entropy . He further states: “It is absolutely obvious that when constructing the principle of the existence of absolute temperature and entropy on the basis of Carathéodory’s theorem, a postulate should be used that would be equivalent to the theorem on the incompatibility of adiabatic and isotherm...” In these corrected constructions, the postulate becomes completely unnecessary Caratheodory, since this postulate is a partial consequence of the necessary theorem on the incompatibility of adiabatic and isotherm."

Method N.I. Belokonya

In justification according to the method of N.I. Belokon's second law of thermodynamics is divided into two principles (laws):

1. The principle of the existence of absolute temperature and entropy ( second law of thermostatics).

2. The principle of increasing entropy( second law of thermodynamics).

Each of these principles was justified on the basis of independent postulates.

• Postulate of the second law of thermostatics (Belokonya).

Temperature is the only state function that determines the direction of spontaneous heat transfer, i.e. between bodies and elements of bodies that are not in thermal equilibrium, simultaneous spontaneous (by balance) transfer of heat in opposite directions is impossible - from bodies more heated to bodies less heated and back. .

The postulate of the second law of thermostatics is a private expression of causality and unambiguity of the laws of nature . For example, if there is a reason due to which in a given system heat moves from a more heated body to a less heated one, then this same reason will prevent the transfer of heat in the opposite direction and vice versa. This postulate is completely symmetrical with respect to the direction of irreversible phenomena, since it does not contain any indications about the observed direction of irreversible phenomena in our world - the world of positive absolute temperatures.

Corollaries of the second law of thermostatics:

Corollary I. Impossible simultaneous(within the same space-time system of positive or negative absolute temperatures) the implementation of complete conversions of heat into work and work into heat.

Corollary II. (the incompatibility theorem between adiabatic and isotherm). On the isotherm of an equilibrium thermodynamic system intersecting two different adiabats of the same system, heat transfer cannot be equal to zero.

Corollary III (theorem of thermal equilibrium of bodies). In equilibrium circular processes of two thermally conjugate bodies (t I = t I I) (\displaystyle (t_(I)=t_(I)I)), forming an adiabatically isolated system, both bodies return to the original adiabats and to the original state simultaneously.

Based on the consequences of the postulate of the second law of thermostatics N.I. Belokon proposed the construction of the principle of the existence of absolute temperature and entropy for reversible and irreversible processes δ Q = δ Q ∗ + Q ∗ ∗ T d S (\displaystyle \delta Q=\delta Q^(*)+Q^(**)TdS)

• Postulate of the second law of thermodynamics (the principle of increasing entropy).

The postulate of the second law of thermodynamics is proposed in the form of a statement that determines the direction of one of the characteristic phenomena in our world of positive absolute temperatures:

Work can be directly and completely converted and heat by friction or electric heating.

Corollary I. Heat cannot be completely converted into work(principle of excluded Perpetuum mobile II kind):

η < 1 {\displaystyle \eta <1}

.

Corollary II. The efficiency or cooling capacity of any irreversible heat engine (engine or refrigerator, respectively) at given temperatures of external sources is always less than the efficiency or cooling capacity of reversible machines operating between the same sources.

A decrease in the efficiency and cooling capacity of real heat engines is associated with a violation of the equilibrium flow of processes (non-equilibrium heat transfer due to the difference in temperatures of heat sources and the working fluid) and the irreversible conversion of work into heat (friction losses and internal resistance).

From this corollary and corollary I of the second law of thermostatics it directly follows that the impossibility of realizing Perpetuum mobile of the I and II types. Based on the postulate of the second law of thermodynamics, the mathematical expression of the second law of classical thermodynamics can be justified as a combined principle of the existence and increase of entropy:

D S ≥ δ Q ∗ T (\displaystyle dS\geq (\frac (\delta Q^(*))(T)))

Natural processes are characterized by directionality and irreversibility, but most of the laws described in this book do not reflect this, at least not explicitly. Breaking eggs and making scrambled eggs is not difficult, but recreating raw eggs from ready-made scrambled eggs is impossible. The smell from an open bottle of perfume fills the room - but you can't put it back into the bottle. And the reason for such irreversibility of processes occurring in the Universe lies in the second law of thermodynamics, which, for all its apparent simplicity, is one of the most difficult and often misunderstood laws of classical physics.

First of all, this law has at least three equally valid formulations, proposed in different years by physicists of different generations. It may seem that there is nothing in common between them, but they are all logically equivalent to each other. From any formulation of the second law, the other two are mathematically derived.

Let's start with the first formulation, which belongs to the German physicist Rudolf Clausius ( cm. Clapeyron-Clausius equation). Here is a simple and clear illustration of this formulation: take an ice cube from the refrigerator and put it in the sink. After some time, the ice cube will melt because the heat from the warmer body (air) is transferred to the colder body (ice cube). From the point of view of the law of conservation of energy, there is no reason for thermal energy to be transferred in exactly this direction: even if the ice became colder and the air warmer, the law of conservation of energy would still be fulfilled. The fact that this does not happen is evidence of the already mentioned direction of physical processes.

We can easily explain why ice and air interact in this way by considering this interaction at the molecular level. From molecular kinetic theory we know that temperature reflects the speed of movement of body molecules - the faster they move, the higher the body temperature. This means that the air molecules move faster than the water molecules in the ice cube. When an air molecule collides with a water molecule on the surface of ice, as experience tells us, fast molecules, on average, slow down, and slow ones accelerate. Thus, the water molecules begin to move faster and faster, or, what is the same, the temperature of the ice increases. This is what we mean when we say that heat is transferred from the air to the ice. And within the framework of this model, the first formulation of the second law of thermodynamics logically follows from the behavior of molecules.

When a body moves over any distance under the influence of a certain force, work is done, and various forms of energy precisely express the ability of the system to produce certain work. Since heat, which represents the kinetic energy of molecules, is a form of energy, it can also be converted into work. But again we are dealing with a directed process. You can convert work into heat with 100% efficiency - you do it every time you press the brake pedal in your car: all the kinetic energy of your car's motion plus the energy you expended on the pedal through the work of your foot and the hydraulic brake system is completely converted into heat released during the friction of the pads on the brake discs. The second formulation of the second law of thermodynamics states that the reverse process is impossible. No matter how much you try to convert all the thermal energy into work, heat losses to the environment are inevitable.

It is not difficult to illustrate the second formulation in action. Imagine the cylinder of your car's internal combustion engine. A high-octane fuel mixture is injected into it, which is compressed by the piston to high pressure, after which it ignites in the small gap between the cylinder head and the free-moving piston, which is tightly fitted to the cylinder walls. During explosive combustion of the mixture, a significant amount of heat is released in the form of hot and expanding combustion products, the pressure of which pushes the piston down. In an ideal world, we could achieve 100% efficiency in the use of released thermal energy, completely converting it into mechanical work of the piston.

In the real world, no one will ever assemble such an ideal engine for two reasons. Firstly, the cylinder walls inevitably heat up as a result of combustion of the working mixture, part of the heat is lost idle and is discharged through the cooling system into the environment. Secondly, part of the work inevitably goes into overcoming the friction force, as a result of which, again, the cylinder walls heat up - another heat loss (even with the best motor oil). Thirdly, the cylinder needs to return to the starting point of compression, and this is also wasted work to overcome friction with the release of heat. As a result, we have what we have, namely: the most advanced heat engines operate with an efficiency of no more than 50%.

This interpretation of the second law of thermodynamics is embedded in Carnot's principle, which is named after the French military engineer Sadi Carnot. It was formulated earlier than others and had a huge influence on the development of engineering technology for many generations to come, although it is of an applied nature. It is acquiring enormous importance from the point of view of modern energy, the most important sector of any national economy. Today, faced with a shortage of fuel resources, humanity, nevertheless, is forced to put up with the fact that the efficiency of, for example, thermal power plants operating on coal or fuel oil does not exceed 30-35% - that is, two thirds of the fuel is burned in vain, or rather consumed to warm the atmosphere - and this in the face of the threat of global warming. That is why modern thermal power plants are easily recognizable by their colossal cooling towers - it is in them that the water that cools the turbines of electric generators is cooled, and excess thermal energy is released into the environment. And such low efficiency of resource use is not the fault, but the misfortune of modern design engineers: they are already squeezing close to the maximum of what the Carnot cycle allows. Those who claim to have found a solution to dramatically reduce thermal energy losses (for example, designed a perpetual motion machine) thereby claim that they have outsmarted the second law of thermodynamics. They might as well claim that they know how to make sure that an ice cube in a sink does not melt at room temperature, but, on the contrary, cools even more, thereby heating the air.

The third formulation of the second law of thermodynamics, usually attributed to the Austrian physicist Ludwig Boltzmann ( cm. Boltzmann's constant is perhaps the best known. Entropy is an indicator of the disorder of the system. The higher the entropy, the more chaotic the movement of the material particles that make up the system. Boltzmann managed to develop a formula for a direct mathematical description of the degree of order of a system. Let's see how it works using water as an example. In the liquid state, water is a rather disordered structure, since the molecules move freely relative to each other, and their spatial orientation can be arbitrary. Ice is another matter - in it the water molecules are ordered, being included in the crystal lattice. The formulation of Boltzmann's second law of thermodynamics, relatively speaking, states that ice, having melted and turned into water (a process accompanied by a decrease in the degree of order and an increase in entropy), will never itself be reborn from water. Once again we see an example of an irreversible natural physical phenomenon.

It is important to understand here that we are not talking about the fact that in this formulation the second law of thermodynamics declares that entropy cannot decrease anywhere and never. Eventually, the melted ice can be placed back into the freezer and re-frozen. The point is that entropy cannot decrease in closed systems- that is, in systems that do not receive external energy supply. A running refrigerator is not an isolated closed-loop system, since it is connected to the power grid and receives energy from the outside - ultimately, from the power plants that produce it. In this case, the closed system will be a refrigerator, plus wiring, plus a local transformer substation, plus a unified power supply network, plus power plants. And since the increase in entropy resulting from random evaporation from power plant cooling towers is many times greater than the decrease in entropy due to the crystallization of ice in your refrigerator, the second law of thermodynamics is in no way violated.

And this, I believe, leads to another formulation of the second principle: The refrigerator does not work unless it is plugged in.

§6 Entropy

Typically, any process in which a system passes from one state to another proceeds in such a way that it is impossible to carry out this process in the opposite direction so that the system passes through the same intermediate states without any changes occurring in the surrounding bodies. This is due to the fact that in the process part of the energy is dissipated, for example, due to friction, radiation, etc. Thus. Almost all processes in nature are irreversible. In any process, some energy is lost. To characterize energy dissipation, the concept of entropy is introduced. ( The entropy value characterizes the thermal state of the system and determines the probability of the implementation of a given state of the body. The more probable a given state is, the greater the entropy.) All natural processes are accompanied by an increase in entropy. Entropy remains constant only in the case of an idealized reversible process occurring in a closed system, that is, in a system in which there is no exchange of energy with bodies external to this system.

Entropy and its thermodynamic meaning:

Entropy- this is a function of the state of the system, the infinitesimal change of which in a reversible process is equal to the ratio of the infinitesimal amount of heat introduced in this process to the temperature at which it was introduced.

In a final reversible process, the change in entropy can be calculated using the formula:

where the integral is taken from the initial state 1 of the system to the final state 2.

Since entropy is a function of state, then the property of the integralis its independence from the shape of the contour (path) along which it is calculated; therefore, the integral is determined only by the initial and final states of the system.

• In any reversible process, the change in entropy is 0

(1)

• In thermodynamics it is proven thatSsystem undergoing an irreversible cycle increases

Δ S> 0 (2)

Expressions (1) and (2) relate only to closed systems; if the system exchanges heat with the external environment, then itsScan behave in any way.

Relations (1) and (2) can be represented as the Clausius inequality

ΔS ≥ 0

those. the entropy of a closed system can either increase (in the case of irreversible processes) or remain constant (in the case of reversible processes).

If the system makes an equilibrium transition from state 1 to state 2, then the entropy changes

Where dU And δAis written for a specific process. According to this formula ΔSdetermined up to an additive constant. It is not entropy itself that has a physical meaning, but the difference in entropies. Let's find the change in entropy in ideal gas processes.

those. entropy changesS Δ S 1→2 of an ideal gas during its transition from state 1 to state 2 does not depend on the type of process.

Because for an adiabatic process δQ = 0, then Δ S= 0 => S= const , that is, an adiabatic reversible process occurs at constant entropy. That is why it is called isentropic.

In an isothermal process (T= const ; T 1 = T 2 : )

In an isochoric process (V= const ; V 1 = V 2 ; )

Entropy has the property of additivity: the entropy of a system is equal to the sum of the entropies of the bodies included in the system.S = S 1 + S 2 + S 3 + ... The qualitative difference between the thermal motion of molecules and other forms of motion is its randomness and disorder. Therefore, to characterize thermal motion, it is necessary to introduce a quantitative measure of the degree of molecular disorder. If we consider any given macroscopic state of a body with certain average values ​​of parameters, then it is something other than a continuous change of close microstates that differ from each other in the distribution of molecules in different parts of the volume and the distributed energy between the molecules. The number of these continuously changing microstates characterizes the degree of disorder of the macroscopic state of the entire system,wis called the thermodynamic probability of a given microstate. Thermodynamic probabilitywstate of a system is the number of ways in which a given state of a macroscopic system can be realized, or the number of microstates that implement a given microstate (w≥ 1, and mathematical probability ≤ 1 ).

As a measure of the surprise of an event, it was agreed to take the logarithm of its probability, taken with a minus sign: the surprise of the state is equal to =-

According to Boltzmann, entropySsystems and thermodynamic probability are related to each other as follows:

Where - Boltzmann constant (). Thus, entropy is determined by the logarithm of the number of states with the help of which a given microstate can be realized. Entropy can be considered as a measure of the probability of the state of the t/d system. Boltzmann's formula allows us to give entropy the following statistical interpretation. Entropy is a measure of the disorder of a system. In fact, the greater the number of microstates realizing a given microstate, the greater the entropy. In the state of equilibrium of the system - the most probable state of the system - the number of microstates is maximum, and entropy is also maximum.

Because real processes are irreversible, then it can be argued that all processes in a closed system lead to an increase in its entropy - the principle of increasing entropy. In the statistical interpretation of entropy, this means that processes in a closed system proceed in the direction of increasing the number of microstates, in other words, from less probable states to more probable ones, until the probability of the state becomes maximum.

§7 Second law of thermodynamics

The first law of thermodynamics, expressing the law of conservation of energy and energy transformation, does not allow us to establish the direction of the flow of t/d processes. In addition, one can imagine many processes that do not contradictIto the beginning t/d, in which energy is conserved, but in nature they are not realized. Possible formulations of the second beginning t/d:

1) the law of increasing entropy of a closed system during irreversible processes: any irreversible process in a closed system occurs in such a way that the entropy of the system increases ΔS≥ 0 (irreversible process) 2) ΔS≥ 0 (S= 0 for reversible and ΔS≥ 0 for an irreversible process)

In processes occurring in a closed system, entropy does not decrease.

2) From Boltzmann's formula S = , therefore, an increase in entropy means a transition of the system from a less probable state to a more probable one.

3) According to Kelvin: a circular process is not possible, the only result of which is the conversion of the heat received from the heater into work equivalent to it.

4) According to Clausius: a circular process is not possible, the only result of which is the transfer of heat from a less heated body to a more heated one.

To describe t/d systems at 0 K, the Nernst-Planck theorem (third law of t/d) is used: the entropy of all bodies in a state of equilibrium tends to zero as the temperature approaches 0 K

From the theorem Nernst-Planck it follows thatC p = C v = 0 at 0 TO

§8 Heat and refrigeration machines.

Carnot cycle and its efficiency

From the formulation of the second law of t/d according to Kelvin it follows that a perpetual motion machine of the second kind is impossible. (A perpetual motion machine is a periodically operating engine that performs work by cooling one heat source.)

Thermostat is a t/d system that can exchange heat with bodies without changing temperature.

Operating principle of a heat engine: from a thermostat with temperature T 1 - heater, the amount of heat is removed per cycleQ 1 , and the thermostat with temperature T 2 (T 2 < T 1) - to the refrigerator, the amount of heat is transferred per cycleQ 2 , while work is done A = Q 1 - Q 2

Circular process or cycle is a process in which a system, having gone through a series of states, returns to its original state. In a state diagram, a cycle is depicted as a closed curve. The cycle performed by an ideal gas can be divided into processes of expansion (1-2) and compression (2-1), the work of expansion is positive A 1-2 > 0, becauseV 2 > V 1 , the compression work is negative A 1-2 < 0, т.к. V 2 < V 1 . Consequently, the work done by the gas per cycle is determined by the area covered by the closed curve 1-2-1. If positive work is done during a cycle (clockwise cycle), then the cycle is called forward, if it is a reverse cycle (the cycle occurs in a counterclockwise direction).

Direct cycle used in heat engines - periodically operating engines that perform work using heat received from outside. The reverse cycle is used in refrigeration machines - periodically operating installations in which, due to the work of external forces, heat is transferred to a body with a higher temperature.

As a result of the circular process, the system returns to its original state and, therefore, the total change in internal energy is zero. ThenІ start t/d for circular process

Q= Δ U+ A= A,

That is, the work done per cycle is equal to the amount of heat received from outside, but

Q= Q 1 - Q 2

Q 1 - quantity heat received by the system,

Q 2 - quantity heat given off by the system.

Thermal efficiency for a circular process is equal to the ratio of the work done by the system to the amount of heat supplied to the system:

For η = 1, the condition must be satisfiedQ 2 = 0, i.e. a heat engine must have one heat sourceQ 1 , but this contradicts the second law of t/d.

The reverse process that occurs in a heat engine is used in a refrigeration machine.

From the thermostat with temperature T 2 the amount of heat is taken awayQ 2 and is transmitted to the thermostat with temperatureT 1 , quantity of heatQ 1 .

Q= Q 2 - Q 1 < 0, следовательно A< 0.

Without doing work, it is impossible to take heat from a less heated body and give it to a more heated one.

Based on the second law of t/d, Carnot derived a theorem.

Carnot's theorem: from all periodically operating heat engines having the same heater temperatures ( T 1) and refrigerators ( T 2), highest efficiency. have reversible machines. Efficiency reversible machines with equal T 1 and T 2 are equal and do not depend on the nature of the working fluid.

A working body is a body that performs a circular process and exchanges energy with other bodies.

The Carnot cycle is a reversible, most economical cycle, consisting of 2 isotherms and 2 adiabats.

1-2 isothermal expansion at T 1 heater; heat is supplied to the gasQ 1 and work is done

2-3 - adiabat. expansion, gas does workA 2-3 >0 above external bodies.

3-4 isothermal compression at T 2 refrigerators; heat is removedQ 2 and work is done;

4-1-adiabatic compression, work is done on the gas A 4-1 <0 внешними телами.

In an isothermal processU= const, so Q 1 = A 12

1

During adiabatic expansionQ 2-3 = 0, and gas work A 23 accomplished by internal energy A 23 = - U

Quantity of heatQ 2 , given by the gas to the refrigerator during isothermal compression is equal to the work of compression A 3-4

2

Adiabatic compression work

Work done as a result of a circular process

A = A 12 + A 23 + A 34 + A 41 = Q 1 + A 23 - Q 2 - A 23 = Q 1 - Q 2

and is equal to the area of ​​the curve 1-2-3-4-1.

Thermal efficiency Carnot cycle

From the adiabatic equation for processes 2-3 and 3-4 we obtain

Then

those. efficiency The Carnot cycle is determined only by the temperatures of the heater and refrigerator. To increase efficiency need to increase the difference T 1 - T 2 .

******************************************************* ******************************************************

In the illustration on the left: protest of Christian conservatives against the second law of thermodynamics. Inscriptions on the posters: the word “entropy” crossed out; “I do not accept the basic tenets of science and vote.”

THE SECOND LAW OF THERMODYNAMICS AND QUESTIONS OF CREATION

In the early 2000s, a group of Christian conservatives gathered on the steps of the Capitol (Kansas, USA) to demand the abolition of a fundamental scientific principle - the second law of thermodynamics (see photo at left). The reason for this was their conviction that this physical law contradicts their faith in the Creator, since it predicts the thermal death of the Universe. The picketers said that they do not want to live in a world moving towards such a future and teach their children this. Leading the campaign against the second law of thermodynamics is none other than a Kansas state senator, who believes that the law "threatens our children's understanding of the universe as a world created by a benevolent and loving God."

It is paradoxical, but in the same USA, another Christian movement - creationists, led by Duane Gish, president of the Institute for Creation Research - on the contrary, not only consider the second law of thermodynamics scientific, but also zealously appeal to it to prove that the world was created by God . One of their main arguments is that life could not arise spontaneously, since everything around is prone to spontaneous destruction rather than creation.

In view of such a striking contradiction between these two Christian movements, a logical question arises - which of them is right? And is anyone even right?

In this article we will look at where it is possible and where it is impossible to apply the second law of thermodynamics and how it relates to issues of faith in the Creator.

WHAT IS THE SECOND LAW OF THERMODYNAMICS

Thermodynamics is a branch of physics that studies the relationships and transformations of heat and other forms of energy. It is based on several fundamental principles called the principles (sometimes the laws) of thermodynamics. Among them, the most famous is probably the second principle.

If we make a short overview of all the principles of thermodynamics, then in brief they are as follows: First start represents the law of conservation of energy as applied to thermodynamic systems. Its essence is that heat is a special form of energy and must be taken into account in the law of conservation and transformation of energy. Second beginning imposes restrictions on the direction of thermodynamic processes, prohibiting the spontaneous transfer of heat from less heated bodies to more heated ones. It also follows from it that it is impossible to convert heat into work with one hundred percent efficiency (losses to the environment are inevitable). It makes it impossible to create a perpetual motion machine based on this. Third beginning states that it is impossible to bring the temperature of any physical body to absolute zero in a finite time, that is, absolute zero is unattainable. Zero (or common) beginning sometimes referred to as the principle according to which an isolated system, regardless of the initial state, eventually comes to a state of thermodynamic equilibrium and cannot leave it on its own. Thermodynamic equilibrium is a state in which there is no transfer of heat from one part of the system to another. (The definition of an isolated system is given below.)

The second law of thermodynamics, in addition to the one given above, has other formulations. All the debates about creation that we mentioned revolve around one of them. This formulation is related to the concept of entropy, which we will have to become familiar with.

Entropy(according to one definition) is an indicator of disorder, or chaos, of a system. In simple terms, the more chaos reigns in a system, the higher its entropy. For thermodynamic systems, the higher the entropy, the more chaotic the movement of the material particles that make up the system (for example, molecules).

Over time, scientists realized that entropy is a broader concept and can be applied not only to thermodynamic systems. In general, any system has a certain amount of chaos, which can change - increase or decrease. In this case, it is appropriate to talk about entropy. Here are some examples:

· Glass of water. If water freezes and turns into ice, then its molecules are connected into a crystal lattice. This corresponds to greater order (less entropy) than the state when the water has melted and the molecules move randomly. However, having melted, the water still retains some form - the glass in which it is located. If water is evaporated, the molecules move even more intensely and occupy the entire volume provided to them, moving even more chaotically. Thus, entropy increases even more.

· Solar system. You can also observe both order and disorder in it. The planets move in their orbits with such precision that astronomers can predict their position at any given time thousands of years in advance. However, there are several asteroid belts in the solar system that move more chaotically - they collide, break up, and sometimes fall on other planets. According to cosmologists, initially the entire solar system (except for the Sun itself) was filled with such asteroids, from which solid planets were later formed, and these asteroids moved even more chaotically than now. If this is true, then the entropy of the solar system (except the Sun itself) was originally higher.

· Galaxy. The galaxy is made up of stars moving around its center. But even here there is a certain amount of disorder: stars sometimes collide, change the direction of movement, and due to mutual influence their orbits are not ideal, changing in a somewhat chaotic manner. So in this system the entropy is not zero.

· Children's room. Those who have small children often have to observe the increase in entropy with their own eyes. After they have done the cleaning, the apartment is in relative order. However, a few hours (and sometimes less) of one or two children staying there in a state of wakefulness is enough for the entropy of this apartment to increase significantly...

If the last example made you smile, then most likely you understand what entropy is.

Returning to the second law of thermodynamics, let us remember that, as we said, it has another formulation that is associated with the concept of entropy. It sounds like this: in an isolated system, entropy cannot decrease. In other words, in any system completely cut off from the surrounding world, disorder cannot spontaneously decrease: it can only increase or, in extreme cases, remain at the same level.

If you put an ice cube in a warm, locked room, it will melt after some time. However, the resulting puddle of water in this room will never itself break back into an ice cube. Open a bottle of perfume there and the smell will spread throughout the room. But nothing will make it go back into the bottle. Light a candle there and it will burn, but nothing will make the smoke turn back into a candle. All these processes are characterized by directionality and irreversibility. The reason for such irreversibility of processes occurring not only in this room, but throughout the entire Universe lies precisely in the second law of thermodynamics.

WHAT DOES THE SECOND LAW OF THERMODYNAMICS APPLY TO?

However, this law, for all its apparent simplicity, is one of the most difficult and often misunderstood laws of classical physics. The fact is that in its formulation there is one word that is sometimes given insufficient attention - this is the word “isolated”. According to the second law of thermodynamics, entropy (chaos) cannot decrease only in isolated systems. This is the law. However, in other systems this is no longer a law, and entropy in them can either increase or decrease.

What is an isolated system? Let's look at what types of systems generally exist from the point of view of thermodynamics:

· Open. These are systems that exchange matter (and possibly energy) with the outside world. Example: a car (consumes gasoline, air, produces heat).

· Closed. These are systems that do not exchange matter with the outside world, but can exchange energy with it. Example: spaceship (sealed, but absorbs solar energy using solar panels).

· Isolated (closed). These are systems that do not exchange either matter or energy with the outside world. Example: thermos (sealed and retains heat).

As we noted, the second law of thermodynamics applies only to the third of the listed types of systems.

To illustrate, let us recall a system consisting of a locked warm room and a piece of ice that melted while in it. In the ideal case, this corresponded to an isolated system, and its entropy increased. However, now let’s imagine that it’s severely frosty outside, and we opened the window. The system became open: cold air began to flow into the room, the temperature in the room dropped below zero, and our piece of ice, which had previously turned into a puddle, froze again.

In real life, a locked room is not an insulated system, because in fact, glass and even bricks allow heat to pass through. And heat, as we noted above, is also a form of energy. Therefore, a locked room is not actually an isolated room, but a closed system. Even if we tightly seal all the windows and doors, the heat will still gradually leave the room, it will freeze and our puddle will also turn into ice.

Another similar example is a room with a freezer. While the freezer is turned off, its temperature is the same as the room temperature. But as soon as you turn it on, it will begin to cool, and the entropy of the system will begin to decrease. This becomes possible because such a system has become closed, that is, it consumes energy from the environment (in this case, electrical).

It is noteworthy that in the first case (a room with a piece of ice), the system released energy to the environment, and in the second (a room with a freezer), on the contrary, it received it. However, the entropy of both systems decreased. This means that in order for the second law of thermodynamics to cease to act as an immutable law, in the general case it is not the direction of energy transfer that is important, but the presence of the very fact of such transfer between the system and the outside world.

EXAMPLES OF DECREASING ENTROPY IN NON-LIVING NATURE. The examples of systems discussed above were created by man. Are there any examples of entropy decreasing in inanimate nature, without the participation of the mind? Yes, as much as you like.

	Snowflakes. During their formation, chaotically moving water vapor molecules combine into an ordered crystal. In this case, cooling occurs, that is, energy is released into the environment, and the atoms occupy a position that is more energetically favorable for them. The crystal lattice of a snowflake corresponds to greater order than chaotically moving vapor molecules.
	Salt crystals. A similar process is observed in an experience that many may remember from their school years. A thread is lowered into a glass with a concentrated solution of salt (for example, table salt or copper sulfate), and soon the chaotically dissolved salt molecules form beautiful figures of bizarre shape.
	Fulgurites. Fulgurite is a shape formed from sand when lightning strikes the ground. In this process, energy (lightning electric current) is absorbed, leading to the melting of the sand, which subsequently solidifies into a solid figure, which corresponds to greater order than chaotically scattered sand.
	Duckweed on the pond. Typically, duckweed growing on the surface of a pond, if there is enough of it, tends to occupy the entire area of ​​the pond. Try to push the duckweed apart with your hands, and in a minute it will return to its place. However, when the wind blows (sometimes barely perceptible), the duckweed accumulates in one part of the pond and is there in a “compressed” state. Entropy decreases due to the absorption of wind energy.
	Formation of nitrogenous compounds. Every year, about 16 million thunderstorms occur in the atmosphere of the globe, during each of which there are tens and hundreds of lightning strikes. During lightning flashes, simple components of the atmosphere - nitrogen, oxygen and moisture - are formed into more complex nitrogen compounds necessary for plant growth. The decrease in entropy in this case occurs due to the absorption of the energy of electrical lightning discharges.
	Butlerov's reaction. This chemical process is also known as autocatalytic synthesis. In it, complex structured sugar molecules in a certain environment grow by themselves, giving rise to their own kind in geometric progression. This is due to the chemical properties of such molecules. The ordering of the chemical structure, and, therefore, the reduction of chaos, in the Butlerov reaction also occurs due to energy exchange with the environment.
	Volcanoes. Chaotically moving magma molecules, breaking out to the surface, solidify into a crystal lattice and form volcanic mountains and rocks of complex shape. If we consider magma as a thermodynamic system, its entropy decreases due to the release of thermal energy into the environment.
	Ozone formation. The most energetically favorable state for oxygen molecules is O 2 . However, under the influence of hard cosmic radiation, a huge number of molecules are converted into ozone (O 3) and can remain in it for quite a long time. This process continues continuously as long as there is free oxygen in the earth's atmosphere.
	Hole in the sand. Everyone knows how dirty the water in our rivers is: it contains garbage, algae, and whatnot, and it’s all mixed up. But next to the shore there is a small hole in the sand, and the water does not pour into it, but seeps through. At the same time, it is filtered: uniformly polluted water is divided into clean and even dirtier water. Entropy obviously decreases, and this happens due to the force of gravity, which, due to the difference in levels, forces water to seep from the river into the hole.
	Puddle. Yes, yes, a simple puddle left after rain also illustrates that entropy can decrease spontaneously! According to the second law of thermodynamics, heat cannot spontaneously transfer from less heated to more heated bodies. However, the temperature of the water in the puddle is consistently kept several degrees lower than the temperature of the soil and surrounding air (you can check this at home with a saucer of water and a thermometer; a hygrometer, consisting of a dry and a wet thermometer, is also based on this principle). Why? Because the puddle evaporates, with faster molecules breaking away from its surface and evaporating, while slower ones remain. Since temperature is related to the speed of molecular movement, it turns out that the puddle is constantly self-cooling in relation to the warmer environment. The puddle, therefore, is an open system, since it exchanges not only energy, but also matter with the environment, and the processes in it clearly go in the direction opposite to that indicated by the second law of thermodynamics.

If you are smart and spend a little time, you can remember and write down thousands of similar examples. It is important to note that in many of the listed cases, a decrease in entropy is not an isolated accident, but a pattern - the tendency towards it is inherent in the very construction of such systems. Therefore, it occurs every time suitable conditions arise, and can continue for a very long time - as long as these conditions exist. All these examples require neither the presence of complex mechanisms that reduce entropy, nor the intervention of the mind.

Of course, if the system is not isolated, then it is not at all necessary that the entropy in it decreases. Rather, on the contrary, it is an increase in entropy, that is, an increase in chaos, that occurs spontaneously more often. In any case, we are accustomed to the fact that any thing left without supervision or care, as a rule, deteriorates and becomes unusable, rather than improved. One can even say that this is a certain fundamental property of the material world - the desire for spontaneous degradation, the general tendency to increase entropy.

However, this subtitle has shown that this general tendency is a law only in isolated systems. In other systems, the increase in entropy is not a law - everything depends on the properties of a particular system and the conditions in which it is located. The second law of thermodynamics cannot be applied to them by definition. Even if entropy increases in one of the open or closed systems, this is not a fulfillment of the second law of thermodynamics, but only a manifestation of the general tendency to increase entropy, which is characteristic of the material world as a whole, but is far from absolute.

THE SECOND LAW OF THERMODYNAMICS AND OUR UNIVERSE

When an enthusiastic observer looks at the starry sky, as well as when an experienced astronomer looks at it through a telescope, they both can observe not only its beauty, but also the amazing order that reigns in this macrocosm.

However, can this order be used to prove that God created the universe? Would it be correct to use this line of reasoning: since the Universe did not fall into chaos in accordance with the second law of thermodynamics, does this prove that it is controlled by God?

Perhaps you are used to thinking that yes. But in fact, contrary to popular belief, no. More precisely, in this regard, it is possible and necessary to use slightly different evidence, but not the second law of thermodynamics.

Firstly, it has not yet been proven that the Universe is an isolated system. Although, of course, the opposite has not been proven, nevertheless, it is not yet possible to unequivocally state that the second law of thermodynamics can be applied to it as a whole.

But let’s say that the isolation of the Universe as a system will be proven in the future (this is quite possible). What then?

Secondly, the second law of thermodynamics does not say what exactly will reign in a particular system - order or chaos. The second law says in which direction this order or disorder will change - in an isolated system, chaos will increase. And in what direction does the order in the Universe change? If we talk about the Universe as a whole, then chaos is increasing in it (as well as entropy). It is important here not to confuse the Universe with individual stars, galaxies or their clusters. Individual galaxies (like our Milky Way) can be very stable structures and appear to not degrade at all over many millions of years. But they are not isolated systems: they constantly radiate energy (such as light and heat) into the surrounding space. Stars burn out and constantly emit matter (“solar wind”) into interstellar space. Thanks to this, a continuous process of transformation of the structured matter of stars and galaxies into chaotically scattered energy and gas occurs in the Universe. What is this if not an increase in entropy?

These degradation processes, of course, occur at a very slow rate, so we do not seem to feel them. But if we were able to observe them at a very accelerated pace - say, a trillion times faster, then a very dramatic picture of the birth and death of stars would unfold before our eyes. It is worth remembering that the first generation of stars that existed since the beginning of the Universe has already died. According to cosmologists, our planet consists of the remnants of the existence and explosion of a once-burnt-out star; As a result of such explosions, all heavy chemical elements are formed.

Therefore, if we consider the Universe to be an isolated system, then the second law of thermodynamics is generally satisfied in it, both in the past and today. This is one of the laws established by God, and therefore it works in the Universe in the same way as other physical laws.

Despite what has been said above, there are many amazing things in the Universe associated with the order reigning in it, but it is not due to the second law of thermodynamics, but to other reasons.

Thus, Newsweek magazine (issue dated November 09, 1998) examined what conclusions discoveries regarding the creation of the Universe lead us to. It said that the facts "show the origin of energy and motion ex nihilo, that is, out of nothing, by a colossal explosion of light and energy, which rather corresponds to the description of [the biblical book] Genesis." Notice how Newsweek magazine explained the similarity of the birth of the Universe with the biblical description of this event.

This magazine writes: “The forces released were - and remain - surprisingly (miraculously?) balanced: if the Big Bang had been a little less violent, the expansion of the Universe would have proceeded more slowly, and soon (in a few million years or in a few minutes - in any case soon ) the process would reverse and collapse would occur. If the explosion had been a little stronger, the Universe could have turned into a too rarefied “liquid broth” and the formation of stars would have been impossible. The chances of our existence were literally astronomically small. The ratio of matter and energy to the volume of space at the Big Bang should have remained within one quadrillionth of one percent of the ideal ratio.”

Newsweek suggested that there was Someone controlling the creation of the Universe, who knew: “Take away even one degree (as mentioned above, the margin of error was one quadrillionth of one percent), ... and the result would be not just disharmony, but eternal entropy and ice."

Astrophysicist Alan Lightman admitted: “That the Universe was created so highly organized is a mystery [to scientists].” He added that “any cosmological theory that aspires to success will eventually have to explain this entropy mystery”: why the universe did not fall into chaos. Obviously, such a low probability of the correct development of events could not be an accident. (Quoted in Awake!, 6/22/99, p. 7.)

THE SECOND LAW OF THERMODYNAMICS AND THE ORIGIN OF LIFE

As noted above, theories are popular among creationists that the second law of thermodynamics proves the impossibility of the spontaneous emergence of life from inanimate matter. Back in the late 1970s - early 1980s, the Institute for Creation Research published a book on this topic and even tried to correspond with the USSR Academy of Sciences on this issue (the correspondence was unsuccessful).

However, as we saw above, the second law of thermodynamics only applies in isolated systems. However, the Earth is not an isolated system, since it constantly receives energy from the Sun and, on the contrary, releases it into space. And a living organism (even, for example, a living cell), in addition, exchanges with the environment and matter. Therefore, the second law of thermodynamics does not apply to this issue by definition.

It was also mentioned above that the material world is characterized by a certain general tendency towards increasing entropy, due to which things are more often destroyed and come into chaos than created. However, as we noted, it is not law. Moreover, if we break away from the macroworld we are accustomed to and plunge into the microworld - the world of atoms and molecules (and it is from here that life is supposed to begin), then we will see that it is much easier to reverse the processes of increasing entropy in it. Sometimes one blind, uncontrolled influence is enough for the entropy of the system to begin to decrease. Our planet is certainly full of examples of such influences: solar radiation in the atmosphere, volcanic heat on the ocean floor, wind on the surface of the earth, and so on. And as a result, many processes flow in the opposite, “unfavorable” direction for them, or the opposite direction becomes “beneficial” for them (for examples, see above in the subtitle “Examples of decreasing entropy in inanimate nature”). Therefore, even our general tendency towards increasing entropy cannot be applied to the emergence of life as some kind of absolute rule: there are too many exceptions to it.

Of course, this does not mean that since the second law of thermodynamics does not prohibit the spontaneous generation of life, then life could arise by itself. There are many other things that make such a process impossible or extremely unlikely, but they are no longer related to thermodynamics and its second law.

For example, scientists managed to obtain several types of amino acids under artificial conditions, simulating the supposed conditions of the Earth’s primary atmosphere. Amino acids are a kind of building blocks of life: in living organisms they are used to build proteins (proteins). However, the proteins necessary for life consist of hundreds, and sometimes thousands of amino acids, connected in a strict sequence and arranged in a special way in a special shape (see the figure on the right). If you combine amino acids in a random order, the probability of creating only one relatively simple functional protein will be negligible - so small that this event will never happen. Assuming their random occurrence is about the same as finding several brick-like stones in the mountains and asserting that a stone house standing nearby was formed from the same stones randomly under the influence of natural processes.

On the other hand, for the existence of life, proteins alone are also not enough: no less complex DNA and RNA molecules are required, the random occurrence of which is also incredible. DNA is essentially a giant storehouse of structured information that is required to make proteins. It is served by a whole complex of proteins and RNA, which copies and corrects this information and uses it “for production purposes.” All this is a single system, the components of which individually do not make any sense, and none of which can be removed from it. One has only to begin to delve deeper into the structure of this system and into the principles of its operation to understand that a Brilliant Designer worked on its creation.

THE SECOND LAW OF THERMODYNAMICS AND FAITH IN THE CREATOR

Is the second law of thermodynamics compatible with faith in the Creator in general? Not just with the fact that he exists, but with the fact that he created the Universe and life on Earth (Genesis 1:1–27; Revelation 4:11); that he promised that the Earth would last forever (Psalm 103:5), which means that both the Sun and the Universe will be eternal in one form or another; that people will live forever in heaven on earth and will never die (Psalm 36:29; Matthew 25:46; Revelation 21:3, 4)?

We can safely say that belief in the second law of thermodynamics is completely compatible with belief in the Creator and his promises. And the reason for this lies in the formulation of this law itself: “in an isolated system, entropy cannot decrease.” Any isolated system remains isolated only as long as no one interferes with its work, including the Creator. But as soon as he intervenes and directs part of his inexhaustible force onto it, the system will cease to be isolated, and the second law of thermodynamics will cease to operate in it. The same can be said about the more general tendency towards increasing entropy, which we discussed above. Yes, it is obvious that almost everything that exists around us - from atoms to the Universe - has a tendency to destruction and degradation over time. But the Creator has the necessary strength and wisdom to stop any processes of degradation and even reverse them when he deems it necessary.

What processes are usually presented by people as making eternal life impossible?

· In a few billion years the Sun will go out. This would have happened if the Creator had never interfered with his work. However, he is the Creator of the Universe and has colossal energy, sufficient to keep the Sun burning forever. For example, it can, by expending energy, reverse the nuclear reactions occurring in the Sun, as if refueling it for several more billion years, and also replenish the volume of matter that the Sun loses in the form of solar wind.

· Sooner or later, the Earth will collide with an asteroid or black hole. No matter how small the probability of this may be, it exists, which means that over the course of eternity it would certainly become a reality. However, God can, using his power, protect the Earth from any harm in advance, simply by preventing such dangerous objects from approaching our planet.

· The moon will fly away from the Earth, and the earth will become uninhabitable. The moon stabilizes the tilt of the earth's axis, thanks to which the climate on it is maintained more or less constant. The Moon is gradually moving away from the Earth, due to which in the future the tilt of its axis could change and the climate could become unbearable. But God, of course, has the necessary power to prevent such destructive changes and keep the Moon in its orbit where He sees fit.

There is no doubt that things in the material world have a tendency to age, degrade and break down. But we must remember that God himself created the world this way. And that means this was part of his plan. The world was not intended to exist forever apart from God. On the contrary, it was created to exist forever under the control of God. And since God had both wisdom and power to create the world, we have no reason to doubt that he has the same power and wisdom to eternally care for his creation, keeping everything in it under his control.

The following Bible verses assure us that the Sun, Moon, Earth and people will exist forever:
· « They will fear you as long as the sun and moon exist - from generation to generation» (Psalm 73:5)
· « [The earth] will not shake forever, forever» (Psalm 103:5)
· « The righteous will inherit the earth and will live on it forever» (Psalm 37:29)

Therefore, nothing prevents us from simultaneously believing in the second law of thermodynamics and considering it a correct scientific principle, and at the same time being deeply religious people and waiting for the fulfillment of all the promises of God recorded in the Bible.

USE HONEST ARGUMENTS

So, if you are a believer, which of the religious groups mentioned at the beginning of the article would you add your voice to? To the participants in the above-described demonstration of Christian conservatives demanding the abolition of the second law of thermodynamics? Or to creationists who use this law as evidence of God's creation of life? I am not for anyone.

Most believers tend to defend their faith in one way or another, and some use the data of science to do this, which largely confirms the existence of the Creator. However, it is important for us to remember one serious biblical principle: “we... want to conduct ourselves honestly in everything” (Hebrews 13:18). Therefore, of course, it would be wrong to use any incorrect arguments to prove the existence of God.

As we have seen from this article, the second law of thermodynamics cannot be used as proof of the existence of God, just as the existence or non-existence of God does not prove or disprove the second law of thermodynamics. The second principle is simply not directly related to the question of the existence of the Creator, just like the vast majority of other physical laws (for example, the law of universal gravitation, the law of conservation of momentum, Archimedes' law or all the other principles of thermodynamics).

God's creations provide us with a large number of convincing evidence, as well as indirect evidence of the existence of the Creator. Therefore, if any of the statements that we previously used as evidence turned out to be incorrect, you should not be afraid to abandon it in order to use only honest arguments to defend your faith.