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

1. Formulation

2. Alternative formulations

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

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

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

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

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

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

Where there is a temperature difference, work can be done

The following expressions are common:

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

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

Every system tends to move from order to disorder.

3. Historical background

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

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

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

4. Statistical interpretation

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

5. Arrow of time

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

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

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

6. Heat death

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

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

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

Second law of thermodynamics

The second law of thermodynamics establishes the criteria for determining the direction of spontaneous processes.

Spontaneous processes that take place in the system without the expenditure of energy from the outside are called.

Processes are reversible and irreversible. irreversible processes proceed spontaneously in only one direction. After these processes, accompanied by changes in the system and the environment, it is impossible to return both the system and environment to the original state.

reversible are the processes after which the system and the environment can be returned to its original state.

The second law of thermodynamics has several formulations, in the version proposed by Clausius, it looks like this: spontaneous transfer of heat from a cold body to a hot one is impossible.

The physical meaning of the second law of thermodynamics is that any spontaneous process proceeds in the direction in which the system passes from a less probable state to a more probable state. In other words, the spontaneous flow of the process is facilitated by an increase in disorder in the system.

To characterize the measure disorder thermodynamic function is used - entropy S, which is associated with thermodynamic probability systems by the Boltzmann formula:

S = k lnW, (25)

where k is the Boltzmann constant.

The thermodynamic probability W is understood as the number of equiprobable microscopic states by which a given macroscopic state of the system can be realized. To determine the thermodynamic probability of the system, it is necessary to find the number various options positions of all particles of the system in space.

Entropy is a quantitative measure of disorder in a system. The more W, the more chaotic the system, the greater the value of entropy. Heating a substance leads to an increase in entropy, and cooling - to a decrease. When approaching absolute zero (-273ºС), the entropy tends to zero, which makes it possible to determine the absolute values ​​of the entropy of various substances, the values ​​of which under standard conditions are presented in the tables. It should be noted that, unlike the enthalpy of formation, the entropy of a simple substance, even in a crystalline state, is not equal to zero, because at a temperature different from absolute zero, the macrostate of a crystal can be realized not by a single macrostate, but by a large number of equiprobable states.

Another formulation of the second law of thermodynamics looks like this: total entropy always increases in a spontaneous process.

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

Equation (26) is a mathematical notation second law of thermodynamics. In this equation, the inequality sign refers to irreversible spontaneous processes, and the equal sign refers to reversible processes.

According to equation (26), the change in entropy during the reversible transition of the system from state 1 to state 2 can be defined as:

ΔS \u003d S 2 - S 1 \u003d. (27)

Phase transitions accompanied by a thermal effect called heat of phase transitionΔN f.p. , and are isothermal processes (T f.p. = const). For a phase transition of one mole of a substance, the change in entropy is:

ΔS f.p. = . (28)

In the processes of melting, evaporation of a liquid, or sublimation of a substance, the entropy increases, since the ordered crystal cell. Reverse processes: crystallization, condensation, desublimation are accompanied by a decrease in disorder in the system, and consequently, a decrease in entropy.

At temperature change substances from T 1 to T 2 at constant pressure, the change in entropy is determined by the formula:

since C p = const, then

ΔS \u003d C p · ln. (thirty)

For isochoric processes

with С v = const

ΔS \u003d C v ln. (32)

standard entropyΔS is the entropy of 1 mole of a substance under standard conditions. Change in standard entropy ΔS during flow chemical reaction can be calculated from the equation, based on the corollary of Hess's law:

The most chaotic form of matter is the gaseous state, therefore, if the number of moles of gas increases as a result of a chemical reaction, then the chaos, and hence the entropy of the system, increases.

Usually, it is not the absolute value of entropy that is determined, but its change (S 2 - S 1) in a particular process. To calculate the change in entropy during the transition of one mole ideal gas formulas are used from one state to another.

Lecture 17

Second law of thermodynamics

Questions

Heat engines and refrigeration machines. Carnot cycle.

Entropy, the second law of thermodynamics.

3. real gases. Van der Waals equation.

Isotherms of real gases. Phase diagram.

4. Internal energy of a real gas.

Joule-Thomson effect.

1. Heat engines and refrigerators. Carnot cycle

cycle called a circular process in which the system, having passed through a series of states, returns to its original position.

direct cycle

- engine efficiency

reverse cycle

- refrigerating coefficient

- heating coefficient

Carnot cycle is the cycle of an ideal engine in which heat is supplied and removed under isothermal conditions at heater temperatures T 1 and refrigerator T 2 , transition from T 1 to T 2 and vice versa is carried out under adiabatic conditions.

A c = A 12 + A 23 + A 34 + A 41 (1)

, (2)

, (3)

, (4)

. (5)

. (6)

(7)

Carnot's theorems:

Efficiency thermal machine operating at given heater and cooler temperatures cannot be greater than the efficiency of a machine operating on a reversible Carnot cycle at the same heater and cooler temperatures.

The efficiency of a heat engine operating according to the Carnot cycle does not depend on the type of working fluid, but dependsonly on the temperatures of the heater and refrigerator.

Dependence of the efficiency of the Carnot cycle on the temperature of the heater(t 2 = 0 o C)

t 1 o C
 t , %

;


, (8)

Carnot's theorem served as the basis for establishing thermodynamic temperature scale, such a thermodynamic scale is not related to the properties of any particular thermometric body.

1. Entropy, second law of thermodynamics

Entropy is the ratio of the heat supplied to the thermodynamic system in some process to the absolute temperature of this body.

(9)

This function was first introduced by S. Carnot under the name reduced heat , then named by Clausius (1865).

, (10)

- heat is supplied

- heat is removed.

Entropy change in particular cases of a polytropic process

1.


isobaric process.

(11)

2 .




isothermal process

1st law of thermodynamics:


(12)

3. Adiabatic process.

isentropic process(13)

4. Isochoric process.

Second law of thermodynamics establishes direction thermal processes.

German physicist's formulation R. Clausiusa: no process is possible, the only result of which would be the transfer of energy by heat transfer from a body with a low temperature to a body with a higher temperature.

English physicist's wording W. Kelvina: v a cyclically operating heat engine cannot process the only result of which would be a transformation into mechanical work the total amount of heat received from a single heat reservoir.

Probabilistic formulation by an Austrian physicist L. Boltzmann: He proposed to consider entropy as measure of statistical disorder closed thermodynamic system. Any state of a system with a large disorder is characterized by a large disorder. Thermodynamic Probability W system states are number of ways, by which the given state of the macroscopic system can be realized, or the number microstates that implement the given macrostate. By definition, the thermodynamic probability W >> 1.

S=k ln W, (14)

where k\u003d 1.38 10 -23 J / K - Boltzmann's constant.

Thus, entropy is determined by the logarithm of the number of microstates with which a macrostate can be realized. Therefore, entropy can be considered as a measure of the probability of the state of a thermodynamic system.

All spontaneous processes in a closed system, bringing the system closer to the state of equilibrium and accompanied by an increase in entropy, are directed towards increasing the probability of the state.

(15)

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

Since entropy increases only in a non-equilibrium process, its increase occurs until the system reaches an equilibrium state. Therefore, the equilibrium state corresponds to the maximum entropy. From this point of view, entropy is a measure of how close a system is to an equilibrium state, i.e. to the state of minimum potential energy.

3. Real gases. Van der Waals equation. Isotherms of real gases. phase diagram

The behavior of a real gas is different from that of an ideal gas. So, the radius of the molecules of most gases is about 10 -10 m (1Ǻ), therefore, the volume of the molecules is about 410 - 30 m 3 . 1 m 3 of gas under normal conditions contains 2.710 25 molecules. Thus, the intrinsic volume of molecules in 1 m 3 under normal conditions will be about 1.210  4 m 3, i.e. about 0.0001 of the volume occupied by the gas.

Any substance, depending on the parameters of the state, can be in different states of aggregation:solid, liquid, gaseous, plasma .

Dutch physicist Van der Waals introduced two amendments to the Mendeleev-Clapeyron equation:

1. Accounting for the intrinsic volume of a molecule

The volume of one molecule: ;

Unavailable volume of a pair of molecules (per molecule):

- quadruple the volume of the molecule.

Unavailable volume for everything N A molecules of one kilomole:

internal pressure;a is the van der Waals constant characterizing the forces of intermolecular attraction.

Van der Waals equation for one mole of gas (Equation of state of real gases):

. (16)

Van der Waals equation for an arbitrary gas mass

. (17)

For fixed values ​​of pressure and temperature, equation (16) has three roots with respect to V(V 1 , V 2 , V 3)

(V   V 1 )(V   V 2)(V   V 3 ) = 0.

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

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

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

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

Formula of the first law of thermodynamics

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

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

Processes of the first law of thermodynamics

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

First law of thermodynamics for an isochoric process

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

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

From this comes the following formula:

Q = ΔU = U (T2) - U (T1).

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

First law of thermodynamics for isobaric process

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

A = p (V2 - V1) = p ∆V.

The isobaric first law of thermodynamics gives:

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

Application of the first law of thermodynamics

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

First law of thermodynamics video

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

Lecture 17

Second law of thermodynamics

Questions

Heat engines and refrigeration machines. Carnot cycle.

Entropy, the second law of thermodynamics.

3. real gases. Van der Waals equation.

Isotherms of real gases. Phase diagram.

4. Internal energy of a real gas.

Joule-Thomson effect.

1. Heat engines and refrigerators. Carnot cycle

cycle called a circular process in which the system, having passed through a series of states, returns to its original position.

direct cycle

- engine efficiency

reverse cycle

- refrigerating coefficient

- heating coefficient

Carnot cycle is the cycle of an ideal engine in which heat is supplied and removed under isothermal conditions at heater temperatures T 1 and refrigerator T 2 , transition from T 1 to T 2 and vice versa is carried out under adiabatic conditions.

A c = A 12 + A 23 + A 34 + A 41 (1)

, (2)

, (3)

, (4)

. (5)

. (6)

(7)

Carnot's theorems:

The efficiency of a heat engine operating at given heater and cooler temperatures cannot be greater than the efficiency of a machine operating on a reversible Carnot cycle at the same heater and cooler temperatures.

The efficiency of a heat engine operating according to the Carnot cycle does not depend on the type of working fluid, but dependsonly on the temperatures of the heater and refrigerator.

Dependence of the efficiency of the Carnot cycle on the temperature of the heater(t 2 = 0 o C)

t 1 o C
 t , %

;


, (8)

Carnot's theorem served as the basis for establishing thermodynamic temperature scale, such a thermodynamic scale is not related to the properties of any particular thermometric body.

1. Entropy, second law of thermodynamics

Entropy is the ratio of the heat supplied to the thermodynamic system in some process to the absolute temperature of this body.

(9)

This function was first introduced by S. Carnot under the name reduced heat , then named by Clausius (1865).

, (10)

- heat is supplied

- heat is removed.

Entropy change in particular cases of a polytropic process

1.


isobaric process.

(11)

2 .




isothermal process

1st law of thermodynamics:


(12)

3. Adiabatic process.

isentropic process(13)

4. Isochoric process.

Second law of thermodynamics establishes direction thermal processes.

German physicist's formulation R. Clausiusa: no process is possible, the only result of which would be the transfer of energy by heat transfer from a body with a low temperature to a body with a higher temperature.

English physicist's wording W. Kelvina: v A cyclically operating heat engine cannot process the only result of which would be the conversion into mechanical work of the entire amount of heat received from a single heat reservoir.

Probabilistic formulation by an Austrian physicist L. Boltzmann: He proposed to consider entropy as measure of statistical disorder closed thermodynamic system. Any state of a system with a large disorder is characterized by a large disorder. Thermodynamic Probability W system states are number of ways, by which the given state of the macroscopic system can be realized, or the number microstates that implement the given macrostate. By definition, the thermodynamic probability W >> 1.

S=k ln W, (14)

where k\u003d 1.38 10 -23 J / K - Boltzmann's constant.

Thus, entropy is determined by the logarithm of the number of microstates with which a macrostate can be realized. Therefore, entropy can be considered as a measure of the probability of the state of a thermodynamic system.

All spontaneous processes in a closed system, bringing the system closer to the state of equilibrium and accompanied by an increase in entropy, are directed towards increasing the probability of the state.

(15)

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).

Since entropy increases only in a non-equilibrium process, its increase occurs until the system reaches an equilibrium state. Therefore, the equilibrium state corresponds to the maximum entropy. From this point of view, entropy is a measure of how close a system is to an equilibrium state, i.e. to the state of minimum potential energy.

3. Real gases. Van der Waals equation. Isotherms of real gases. phase diagram

The behavior of a real gas is different from that of an ideal gas. So, the radius of the molecules of most gases is about 10 -10 m (1Ǻ), therefore, the volume of the molecules is about 410 - 30 m 3 . 1 m 3 of gas under normal conditions contains 2.710 25 molecules. Thus, the intrinsic volume of molecules in 1 m 3 under normal conditions will be about 1.210  4 m 3, i.e. about 0.0001 of the volume occupied by the gas.

Any substance, depending on the parameters of the state, can be in different states of aggregation:solid, liquid, gaseous, plasma .

Dutch physicist Van der Waals introduced two amendments to the Mendeleev-Clapeyron equation:

1. Accounting for the intrinsic volume of a molecule

The volume of one molecule: ;

Unavailable volume of a pair of molecules (per molecule):

- quadruple the volume of the molecule.

Unavailable volume for everything N A molecules of one kilomole:

internal pressure;a is the van der Waals constant characterizing the forces of intermolecular attraction.

Van der Waals equation for one mole of gas (Equation of state of real gases):

. (16)

Van der Waals equation for an arbitrary gas mass

. (17)

For fixed values ​​of pressure and temperature, equation (16) has three roots with respect to V(V 1 , V 2 , V 3)

(V   V 1 )(V   V 2)(V   V 3 ) = 0.