One of the basic laws of physics, the law of non-decreasing entropy in an isolated system.
For a constant temperature system there is specific function state S - entropy, which is defined in such a way that
1. An adiabatic transition from equilibrium state A to equilibrium state B is possible only when

2. The increase in entropy in a slow quasi-static process is equal to

Where T is temperature.
The above formulation is very formal. There are many alternative formulations of the second law of thermodynamics. For example, Planck proposed the following formulation:
It is impossible to build a machine that cycles, cools a heat source, or lifts loads without causing however, no changes in nature.

Constantine Carathéodory gave an axiomatically strict formulation
Near state 1, such states 2 exist; adiabatic transitions from state 1 to state 2 are impossible.

Boltzmann formulated the second law of thermodynamics from the point of view of statistical physics:
Nature tends to move from states with a lower probability of implementation to states with a higher probability of implementation.

Such formulations are common.
It is impossible to be an eternal mover of another 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.

The second law of thermodynamics was formulated in the mid-19th century, at a time when the theoretical basis for the design and construction of heat engines was being created. The experiments of Mayer and Joule established the equivalence between thermal and mechanical energies (the first law of thermodynamics). The question arose about the efficiency of heat engines. Experimental studies have shown that some 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, introducing a new definition for entropy, which was based on microscopic atomistic concepts.
Statistical physics introduces a new definition of entropy, which at first glance is very different from the definition of thermodynamics. It is given by the Boltzmann formula:

Where? - the number of microscopic states corresponding to a given macroscopic state, k B- Boltzmann constant.
From the statistical definition of entropy it is obvious that an increase in entropy corresponds to a transition to a macroscopic state that is characterized highest value microscopic states.
If the initial state of a thermodynamic system is nonequilibrium, then over time it moves to an equilibrium state, increasing its entropy. This process occurs only in one direction. The reverse process - the transition from an equilibrium state to an initial nonequilibrium state - is not realized. That is, the flow of time receives direction.
The laws of physics that describe the microscopic world are invariant under the replacement of t by -t. This statement is true both for the laws of classical mechanics and the laws of quantum mechanics. In the microscopic world, conservative forces act; there is no friction, which is the dissipation of energy, i.e. the transformation of other types of energy into the energy of thermal motion, and this in turn is associated with the law of non-decreasing entropy.
Imagine, for example, a gas in a reservoir placed in a larger reservoir. If you open the valve of the smaller tank, the gas will after some time fill the larger tank so that its density is equalized. 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 container. But in the macroscopic world this never happens.
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 considerations that appeared after the establishment of the second law of thermodynamics, called heat 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 conversion into heat, to more and more disorder. Of course, our Universe is still quite young. Thermonuclear processes in stars lead to a steady flow of energy to Earth, for example. The Earth is and will remain an open system for a long time, which receives energy from various sources: from the Sun, from processes radioactive decay in the core, i.e. In open systems, entropy can decrease, which leads to the emergence of a variety of comfortable structures.

Introduction_3

General characteristics and formulation of the second law of thermodynamics 4

The concept of entropy_ 8

Conclusion_ 10

References_ 11

Introduction

Currently, thermal power and thermal installations have become widespread in various industries national economy. In industrial enterprises they form the main important part of technological equipment.

The science that studies methods of using fuel energy, the laws of processes of changing the state of matter, the principles of operation of various machines and devices, energy and technological installations is called thermal engineering. Theoretical foundations Thermal engineering is thermodynamics and heat transfer theory.

Thermodynamics is based on fundamental laws (principles), which are a generalization of observations of processes occurring in nature regardless of the specific properties of bodies. This explains the universality of patterns and relationships between physical quantities obtained from thermodynamic studies.

The first law of thermodynamics characterizes and describes the processes of energy conversion from the quantitative side and provides everything necessary for drawing up the energy balance of any installation or process.

The second law of thermodynamics, being the most important law of nature, determines the direction in which thermodynamic processes proceed, establishes possible limits for the conversion of heat into work in circular processes, and allows us to give a strict definition of concepts such as entropy, temperature, etc. In this regard, the second law of thermodynamics significantly complements the first.

The principle of the unattainability of absolute zero is accepted as the third law of thermodynamics.

The theory of heat transfer studies the patterns of heat transfer from one region of space to another. Heat transfer processes are processes of exchange of internal energy between the elements of the system under consideration in the form of heat.

General characteristics and formulation of the second law of thermodynamics

Natural processes are always directed towards the system achieving an equilibrium state (mechanical, thermal or any other). This phenomenon is reflected by the second law of thermodynamics, which has great value and for analyzing the operation of thermal power machines. In accordance with this law, for example, heat can spontaneously transfer only from a body with higher temperature to a body with a lower temperature. To carry out the reverse process, some work must be expended. In this regard, the second law of thermodynamics can be formulated as follows: a process in which heat would transfer spontaneously from colder bodies to warmer bodies is impossible (postulate of Clausius, 1850).

The second law of thermodynamics also determines the conditions under which heat can be converted into work for as long as desired. In any open thermodynamic process, as the volume increases, positive work is done:

,

where l is the final work,

v 1 and v 2 are the initial and final specific volume, respectively;

but the expansion process cannot continue indefinitely, therefore, the possibility of converting heat into work is limited.

The continuous conversion of heat into work is carried out only in a circular process or cycle.

Each elementary process included in the cycle is carried out when heat is supplied or removed dQ, accompanied by the completion or expenditure of work, an increase or decrease internal energy, but always when the condition is met dQ= dU+ dL And dq= du+ dl, which shows that without heat supply ( dq=0) external work can only be done due to the internal energy of the system, and the supply of heat to a thermodynamic system is determined by the thermodynamic process. Closed loop integration gives:

, , because .

Here Q C And L C- respectively, the heat converted into work in the cycle and the work done by the working fluid, which is the difference | L 1 | - |L 2| positive and negative works of elementary processes of the cycle.

The elementary amount of heat can be considered as supplied ( dQ>0) and diverted ( dQ<0) from the working fluid. The sum of heat supplied in the cycle |Q 1 |, and the sum of heat removed |Q 2 |. Hence,

L C =Q C =|Q 1 | - |Q 2 |.

The supply of heat quantity Q 1 to the working fluid is possible in the presence of an external source with a temperature higher than the temperature of the working fluid. This heat source is called hot. Removal of the amount of heat Q 2 from the working fluid is also possible in the presence of an external heat source, but with a temperature lower than the temperature of the working fluid. Such a heat source is called cold. Thus, to complete a cycle, it is necessary to have two sources of heat: one with a high temperature, the other with a low temperature. In this case, not all of the expended amount of heat Q 1 can be converted into work, since the amount of heat Q 2 is transferred to a cold source.

The operating conditions of a heat engine are as follows:

The need for two heat sources (hot and cold);

Cyclic operation of the engine;

Transfer of part of the amount of heat received from a hot source to a cold one without converting it into work.

In this regard, the second law of thermodynamics can be given several more formulations:

- transfer of heat from a cold source to a hot one is impossible without the cost of work;

- it is impossible to build a periodically operating machine that performs work and, accordingly, cools the thermal reservoir;

- nature strives for a transition from less probable states to more probable ones.

It should be emphasized that the second law of thermodynamics (like the first) is formulated on the basis of experience.

In the most general view The second law of thermodynamics can be stated as follows: any real spontaneous process is irreversible. All other formulations of the second law are special cases of the most general formulation.

W. Thomson (Lord Kelvin) proposed the following formulation in 1851: It is impossible, by means of an inanimate material agent, to obtain mechanical work from any mass of matter by cooling it below the temperature of the coldest surrounding object.

M. Planck proposed a formulation that was clearer than Thomson’s: It is impossible to build a periodically operating machine, the entire operation of which would be reduced to the concept of a certain load and cooling of a heat source. A periodically operating machine should be understood as an engine that continuously (in a cyclic process) converts heat into work. In fact, if it were possible to build a heat engine that would simply take heat from some source and continuously (cyclically) transform it into work, then this would contradict the position that work can be produced by a system only when there is no equilibrium (in particular, in relation to a heat engine - when there is a temperature difference between hot and cold sources in the system).

If there were no restrictions imposed by the second law of thermodynamics, this would mean that it was possible to build a heat engine with only one heat source. Such an engine could operate by cooling, for example, water in the ocean. This process could continue until all the internal energy of the ocean was converted into work. A heat engine that would act in this way was aptly named by V.F. Ostwald perpetual motion machine of the second kind (in contrast to a perpetual motion machine of the first kind, which works contrary to the law of conservation of energy). In accordance with the above, the formulation of the second law of thermodynamics given by Planck can be modified as follows: the implementation of a perpetual motion machine of the second kind is impossible.

It should be noted that the existence of a perpetual motion machine of the second kind does not contradict the first law of thermodynamics; in fact, in this engine, work would be produced not from nothing, but due to the internal energy contained in the heat source, so that from the quantitative side, the process of obtaining work from heat in this case would not be impossible. However, the existence of such an engine is impossible from the point of view of the qualitative side of the process of heat transfer between bodies.

The concept of entropy

The discrepancy between the transformation of heat into work and work into heat leads to a one-sided direction of real processes in nature, which reflects the physical meaning of the second law of thermodynamics in the law on the existence and increase in real processes of a certain function called entropy , defining measure of energy depreciation.

Often the second law of thermodynamics is presented as a unified principle of the existence and increase of entropy.

The laws of thermodynamics are also called its principles. In fact, the beginning of thermodynamics is nothing more than a set of certain postulates that underlie the corresponding section of molecular physics. These provisions were established during scientific research. At the same time, they were proven experimentally. Why are the laws of thermodynamics accepted as postulates? The whole point is that in this way thermodynamics can be constructed in an axiomatic way.

Basic laws of thermodynamics

A little about structuring. The laws of thermodynamics are divided into four groups, each of which has a specific meaning. So, what can the principles of thermodynamics tell us?

First and second

The first beginning will tell you how the law of conservation of energy is applied in relation to a particular thermodynamic system. The second law puts forward certain restrictions that apply to the directions of thermodynamic processes. More specifically, they prohibit the spontaneous transfer of heat from a less heated to a more heated body. The second law of thermodynamics also has an alternative name: the law of increasing entropy.

Third and fourth

The third law describes the behavior of entropy near absolute temperature zero. There is one more beginning, the last one. It is called the “zero law of thermodynamics.” Its meaning is that any closed system will come to a state of thermodynamic equilibrium and will no longer be able to exit it on its own. Moreover, its initial state can be any.

Why are the principles of thermodynamics needed?

The laws of thermodynamics were studied in order to describe the macroscopic parameters of certain systems. At the same time, specific proposals related to the microscopic device are not put forward. This issue is studied separately, but by another branch of science - statistical physics. The laws of thermodynamics are independent of each other. What could this mean? This must be understood in such a way that it is impossible to derive any one principle of thermodynamics from another.

First law of thermodynamics

As is known, a thermodynamic system is characterized by several parameters, including internal energy (denoted by the letter U). The latter is formed from the kinetic energy that all particles have. This can be the energy of translational, as well as oscillatory and rotational motion. At this point, let us remember that energy can be not only kinetic, but also potential. So, in the case of ideal gases, potential energy is neglected. That is why the internal energy U will consist solely of the kinetic energy of molecular motion and depend on temperature.

This quantity - internal energy - is called in other words the state function, since it is determined by the state of the thermodynamic system. In our case, it is determined by the gas temperature. It should be noted that the internal energy does not depend on what the transition to the state was. Let us assume that the thermodynamic system undergoes a circular process (cycle, as it is called in molecular physics). In other words, the system, having left the initial state, undergoes certain processes, but as a result returns to the primary state. Then it is not difficult to guess that the change in internal energy will be equal to 0.

How does internal energy change?

There are two ways to change the internal energy of an ideal gas. The first option is to do the work. The second is to provide the system with a certain amount of heat. It is logical that the second method involves not only the imparting of heat, but also its removal.

Statement of the first law of thermodynamics

There may be several of them (formulations), since everyone likes to speak differently. But in fact the essence remains the same. It boils down to the fact that the amount of heat that was supplied to the thermodynamic system is spent on making the ideal gas mechanical work and change in internal energy. If we talk about the formula or mathematical notation of the first law of thermodynamics, it looks like this: dQ = dU + dA.

All quantities that are part of the formula can have different signs. Nothing prevents them from being negative. Let us assume that an amount of heat Q is supplied to the system. Then the gas will heat up. The temperature increases, which means the internal energy of the gas also increases. That is, both Q and U will have positive values. But if the internal energy of the gas increases, it begins to behave more actively and expand. Therefore, the work will also be positive. We can say that the work is done by the system itself, the gas.

If a certain amount of heat is taken from the system, the internal energy decreases and the gas contracts. In this case, we can already say that work is done on the system, and not by the system itself. Suppose again that some thermodynamic system undergoes a cycle. In this case (as mentioned earlier), the change in internal energy will be equal to 0. This means that the work done by or on the gas will be numerically equal to the heat supplied or removed to the system.

The mathematical notation of this consequence is called another formulation of the first law of thermodynamics. It roughly goes like this: “In nature, it is impossible for an engine of the first kind to exist, that is, an engine that would do work that exceeds the heat received from the outside.”

Second law of thermodynamics

It is not difficult to guess that thermodynamic equilibrium is characteristic of a system in which macroscopic quantities remain unchanged over time. This, of course, is the pressure, volume and temperature of the gas. Their immutability can be built on several conditions: the absence of thermal conductivity, chemical reactions, diffusion and other processes. If, under the influence of external factors, the system was taken out of thermodynamic equilibrium, it will return to it over time. But if these factors are absent. And this will happen spontaneously.

We will take a slightly different path, different from what many textbooks recommend. First, let's get acquainted with the second law of thermodynamics, and only then we will figure out what kind of quantities are included in it and what they mean. So, in a closed system, in the presence of any processes occurring in it, entropy does not decrease. The second law of thermodynamics is written as follows: dS >(=) 0. Here the > sign will be associated with an irreversible process, and the = sign with a reversible one.

What is called a reversible process in thermodynamics? And this is a process in which the system returns (after a series of processes) to its original state. Moreover, in this case, no changes remain either in the system or in the environment. In other words, a reversible process is a process for which it is possible to return to the initial state through intermediate states identical to the direct process. There are very few such processes in molecular physics. For example, the transfer of heat from a more heated body to a less heated one will be irreversible. The same is true in the case of diffusion of two substances, as well as the spread of gas over the entire volume.

Entropy

Entropy, which occurs in the second law of thermodynamics, is equal to the change in heat divided by temperature. Formula: dS = dQ/T. It has certain properties.

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

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

Where Q 1 – amount of heat imparted to the working fluid at temperature T 1 from the heater; Q 2 – amount of heat given off by the working fluid at temperature T 2 refrigerator.

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

Clausius(1850) formulated second law of thermodynamics So: a process in which heat would spontaneously transfer from colder bodies to hotter bodies is impossible.

W. Thomson (Kelvin)(1851) proposed the following formulation: It is impossible to build a periodically operating machine, all of whose activity would be reduced to performing mechanical work and corresponding cooling of the reservoir.

Thomson's postulate can be formulated as follows: a perpetual motion machine of the second kind is impossible. Perpetual motion machine the second type 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 from 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 turns into heat completely without any compensation. The latter is associated, as noted earlier, with the spontaneous process of energy dissipation (depreciation).

The second law of thermodynamics introduces the system state function, which 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 as follows to the heat entering the system and the temperature of the system:

For reversible processes; (3.2)

For irreversible processes. (3.3)

Thus, during reversible processes in an adiabatically isolated system, its entropy does not change (dS = 0), and during irreversible processes it increases (dS > 0).

In contrast to internal energy, the value of entropy of an isolated system depends on the nature of the processes occurring in it: During relaxation, the entropy of an isolated system should increase, reaching maximum value at equilibrium.

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

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

Thus the second law of thermodynamics gives criterion for spontaneous 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. This means that in a state of equilibrium the entropy of an isolated system is maximum. In accordance with this the criterion for equilibrium in an isolated system will be

If you take part in the process non-isolated system, That to assess the irreversibility (spontaneity) of the process, it is necessary to know the change in entropy of the system dS 1 and entropy change environment dS 2. If we accept that system and environment(they are often called "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 we can equate δQ = dU and it doesn’t matter whether the transfer of heat occurs reversibly or irreversibly, since δQ arr, and δQ roughly equal dU environment. Thus, the change in entropy of the environment is always equal.

The pattern of heat transfer from one object to another is considered in the statement about heat transfer. The whole process consists of an internal exchange of energy between objects, which is called heat.

The correct process is aimed only at obtaining an equal state, be it thermal, mechanical or any other. This action is contained in the second law of thermodynamics, which is of great importance for heat engines. This law says that heat can move on its own exclusively from an object with a high temperature to an object lowest temperature. To carry out the reverse cycle, some work will be expended. From which we can derive the conclusion of the second law of thermodynamics: This action during which heat itself moves from an object with less heat to an object with the greatest heat cannot exist.

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At one time, the second law of thermodynamics gives an assessment of the conditions under which heat can be used and how much it wants to be used. Any open thermodynamic action during volume increase will work with a plus sign.

Formula of the second law of thermodynamics

In which L- will be the final work, v1 and v2- their own initial and final specific volume.
Since the action of expansion cannot be infinite, accordingly, the conversion of heat into work will be limited by this. This action will be continuous in the case of closed circular motion.

Any action occurring in a cycle occurs with the supply or removal of heat dQ, accompanied by the cost or performance of work, a decrease or increase in energy inside the body, and a prerequisite dQ=dU+dL , dg=du+d1 must be carried out. After all, it proves that without heat (dg=0) all actions will occur due to the internal energy of the system, and the input of heat into the system can be determined by thermodynamics.

Closed loop integration:

in which Qt, Lt - will be the heat converted into work, L1- L2 - the work done by this body. Q1 is heat supplied, Q2 is heat removed. This means Lts = Qts = Q1-Q2
Heat can be supplied to body Q1 only in the presence of a hotter body, and heat can be removed from Q2 only in the presence of a colder body. If the process is cyclical, you will need two sources with different temperatures.