Thermodynamics (Greek θέρμη - “heat”, δύναμις - “force”) is a branch of physics that studies the most general properties of macroscopic systems and methods of transfer and transformation of energy in such systems.
In thermodynamics, states and processes are studied, to describe which the concept of temperature can be introduced. Thermodynamics (T.) is a phenomenological science based on generalizations of experimental facts. The processes occurring in thermodynamic systems are described by macroscopic quantities (temperature, pressure, concentrations of components), which are introduced to describe systems consisting of a large number of particles and are not applicable to individual molecules and atoms, unlike, for example, the quantities introduced in mechanics or electrodynamics.
Modern phenomenological thermodynamics is a rigorous theory developed on the basis of several postulates. However, the connection of these postulates with the properties and laws of interaction of particles from which thermodynamic systems are built is given by statistical physics. Statistical physics also makes it possible to clarify the limits of applicability of thermodynamics.
The laws of thermodynamics are general in nature and do not depend on specific details of the structure of matter at the atomic level. Therefore, thermodynamics is successfully applied in a wide range of science and technology issues, such as energy, heat engineering, phase transitions, chemical reactions, transport phenomena and even black holes. Thermodynamics is important for a wide variety of areas of physics and chemistry, chemical technology, aerospace engineering, mechanical engineering, cell biology, biomedical engineering, materials science, and even finds its application in areas such as economics.
Important years in the history of thermodynamics
- The origin of thermodynamics as a science is associated with the name of G. Galilei, who introduced the concept of temperature and designed the first device that responded to changes in ambient temperature (1597).
- Soon G. D. Fahrenheit (1714), R. Reaumur (1730) and A. Celsius (1742) created temperature scales in accordance with this principle.
- J. Black in 1757 already introduced the concepts of latent heat of fusion and heat capacity (1770). And Wilcke (J. Wilcke, 1772) introduced the definition of calorie as the amount of heat required to heat 1 g of water by 1 °C.
- Lavoisier (A. Lavoisier) and Laplace (P. Laplace) designed a calorimeter in 1780 (see Calorimetry) and for the first time experimentally determined the beat. heat capacity of a number of substances.
- In 1824, S. Carnot (N. L, S. Carnot) published a work devoted to the study of the principles of operation of heat engines.
- B. Clapeyron introduced a graphical representation of thermodynamic processes and developed the method of infinitesimal cycles (1834).
- G. Helmholtz noted the universal nature of the law of conservation of energy (1847). Subsequently, R. Clausius and W. Thomson (Kelvin; W. Thomson) systematically developed the theoretical apparatus of thermodynamics, which is based on the first law of thermodynamics and the second law of thermodynamics.
- The development of the 2nd principle led Clausius to the definition of entropy (1854) and the formulation of the law of increasing entropy (1865).
- Beginning with the work of J. W. Gibbs (1873), who proposed the method of thermodynamic potentials, the theory of thermodynamic equilibrium has been developed.
- In the 2nd half. 19th century studies of real gases were carried out. A special role was played by the experiments of T. Andrews, who first discovered the critical point of the liquid-vapor system (1861), its existence was predicted by D. I. Mendeleev (1860).
- By the end of the 19th century. great strides were made in obtaining low temperatures, as a result of which O2, N2 and H2 were liquefied.
- In 1902, Gibbs published a work in which all the basic thermodynamic relations were obtained within the framework of statistical physics.
- The connection between kinetic properties of the body and its thermodynamic. characteristics were established by L. Onsager (L. Onsager, 1931).
- In the 20th century intensively studied the thermodynamics of solids, as well as quantum liquids and liquid crystals, in which diverse phase transitions take place.
- L. D. Landau (1935-37) developed a general theory of phase transitions based on the concept of spontaneous symmetry breaking.
Sections of thermodynamics
Modern phenomenological thermodynamics is usually divided into equilibrium (or classical) thermodynamics, which studies equilibrium thermodynamic systems and processes in such systems, and nonequilibrium thermodynamics, which studies nonequilibrium processes in systems in which the deviation from thermodynamic equilibrium is relatively small and still allows for thermodynamic description.
Equilibrium (or classical) thermodynamics
In equilibrium thermodynamics, variables such as internal energy, temperature, entropy, and chemical potential are introduced. All of them are called thermodynamic parameters (quantities). Classical thermodynamics studies the relationships of thermodynamic parameters with each other and with physical quantities introduced into consideration in other branches of physics, for example, with the gravitational or electromagnetic field acting on the system. Chemical reactions and phase transitions are also included in the study of classical thermodynamics. However, the study of thermodynamic systems in which chemical transformations play a significant role is the subject of chemical thermodynamics, and thermal engineering deals with technical applications.
Classical thermodynamics includes the following sections:
- principles of thermodynamics (sometimes also called laws or axioms)
- equations of state and properties of simple thermodynamic systems (ideal gas, real gas, dielectrics and magnets, etc.)
- equilibrium processes with simple systems, thermodynamic cycles
- nonequilibrium processes and the law of non-decreasing entropy
- thermodynamic phases and phase transitions
In addition, modern thermodynamics also includes the following areas:
- a rigorous mathematical formulation of thermodynamics based on convex analysis
- non-extensive thermodynamics
In systems that are not in a state of thermodynamic equilibrium, for example, in a moving gas, the local equilibrium approximation can be used, in which it is assumed that the equilibrium thermodynamic relations are satisfied locally at each point of the system.
Nonequilibrium thermodynamics
In nonequilibrium thermodynamics, variables are considered as local not only in space, but also in time, that is, time can enter its formulas explicitly. Let us note that Fourier’s classic work “Analytical Theory of Heat” (1822), dedicated to the issues of thermal conductivity, was ahead of not only the emergence of nonequilibrium thermodynamics, but also Carnot’s work “Reflections on the driving force of fire and on machines capable of developing this force” (1824), which is generally considered a starting point in the history of classical thermodynamics.
Basic concepts of thermodynamics
Thermodynamic system- a body or group of bodies interacting, mentally or actually isolated from the environment.
Homogeneous system– a system within which there are no surfaces separating parts of the system (phases) that differ in properties.
Heterogeneous system- a system within which there are surfaces separating parts of the system that differ in properties.
Phase– a set of homogeneous parts of a heterogeneous system, identical in physical and chemical properties, separated from other parts of the system by visible interfaces.
Isolated system- a system that does not exchange either matter or energy with the environment.
Closed system- a system that exchanges energy with the environment, but does not exchange matter.
Open system- a system that exchanges both matter and energy with the environment.
The totality of all physical and chemical properties of a system characterizes it thermodynamic state. All quantities characterizing any macroscopic property of the system under consideration are status parameters. It has been experimentally established that to unambiguously characterize a given system it is necessary to use a certain number of parameters called independent; all other parameters are considered as functions of independent parameters. Parameters that can be directly measured, such as temperature, pressure, concentration, etc., are usually chosen as independent state parameters. Any change in the thermodynamic state of a system (change in at least one state parameter) is thermodynamic process.
Reversible process- a process that allows the system to return to its original state without any changes remaining in the environment.
Equilibrium process– a process in which a system passes through a continuous series of equilibrium states.
Energy– a measure of the system’s ability to do work; a general qualitative measure of the movement and interaction of matter. Energy is an integral property of matter. A distinction is made between potential energy, caused by the position of a body in a field of certain forces, and kinetic energy, caused by a change in the position of the body in space.
Internal energy of the system– the sum of the kinetic and potential energy of all particles that make up the system. You can also define the internal energy of a system as its total energy minus the kinetic and potential energy of the system as a whole.
Forms of energy transition
Forms of energy transfer from one system to another can be divided into two groups.
- The first group includes only one form of transition of motion through chaotic collisions of molecules of two contacting bodies, i.e. by thermal conduction (and at the same time by radiation). The measure of the movement transmitted in this way is heat. Heat is a form of energy transfer through the disordered movement of molecules.
- The second group includes various forms of transition of motion, the common feature of which is the movement of masses covering very large numbers of molecules (i.e., macroscopic masses) under the influence of any forces. These are the lifting of bodies in a gravitational field, the transition of a certain amount of electricity from a higher electrostatic potential to a smaller one, the expansion of a gas under pressure, etc. The general measure of motion transmitted by such methods is work - a form of energy transfer through the ordered movement of particles.
Heat and work characterize qualitatively and quantitatively two different forms of transfer of motion from a given part of the material world to another. Heat and work cannot be contained in the body. Heat and work arise only when a process occurs, and characterize only the process. Under static conditions, heat and work do not exist. The difference between heat and work, accepted by thermodynamics as the starting position, and the opposition of heat to work makes sense only for bodies consisting of many molecules, because for one molecule or for a collection of few molecules, the concepts of heat and work lose their meaning. Therefore, thermodynamics considers only bodies consisting of a large number of molecules, i.e. so-called macroscopic systems.
Three principles of thermodynamics
The principles of thermodynamics are a set of postulates underlying thermodynamics. These provisions were established as a result of scientific research and were proven experimentally. They are accepted as postulates so that thermodynamics can be constructed axiomatically.
The need for the principles of thermodynamics is due to the fact that thermodynamics describes the macroscopic parameters of systems without specific assumptions regarding their microscopic structure. Statistical physics deals with issues of internal structure.
The principles of thermodynamics are independent, that is, none of them can be derived from the other principles. Analogues of Newton's three laws in mechanics are the three principles in thermodynamics, which connect the concepts of “heat” and “work”:
- The zero law of thermodynamics speaks of thermodynamic equilibrium.
- The first law of thermodynamics is about the conservation of energy.
- The second law of thermodynamics is about heat flows.
- The third law of thermodynamics is about the unattainability of absolute zero.
General (zero) law of thermodynamics
The general (zero) law of thermodynamics states that two bodies are in a state of thermal equilibrium if they can transfer heat to each other, but this does not happen.
It is not difficult to guess that two bodies do not transfer heat to each other if their temperatures are equal. For example, if you measure the temperature of a human body using a thermometer (at the end of the measurement, the temperature of the person and the temperature of the thermometer will be equal), and then, using the same thermometer, measure the temperature of the water in the bathroom, and it turns out that both temperatures coincide (there is thermal equilibrium between the person and thermometer and a thermometer with water), we can say that a person is in thermal equilibrium with the water in the bath.
From the above, we can formulate the zero law of thermodynamics as follows: two bodies that are in thermal equilibrium with a third are also in thermal equilibrium with each other.
From a physical point of view, the zero law of thermodynamics sets the reference point, since there is no heat flow between two bodies that have the same temperature. In other words, we can say that temperature is nothing more than an indicator of thermal equilibrium.
First law of thermodynamics
The first law of thermodynamics is the law of conservation of thermal energy, which states that energy does not disappear without leaving a trace.
The system can either absorb or release thermal energy Q, while the system performs work W on the surrounding bodies (or the surrounding bodies perform work on the system), and the internal energy of the system, which had the initial value Uninit, will be equal to Uend:
Uend-Ustart = ΔU = Q-W
Thermal energy, work and internal energy determine the total energy of the system, which is a constant value. If a certain amount of thermal energy Q is transferred to (taken away) from the system, in the absence of work, the amount of internal energy of the system U will increase (decrease) by Q.
Second law of thermodynamics
The second law of thermodynamics states that thermal energy can move only in one direction - from a body with a higher temperature to a body with a lower temperature, but not vice versa.
Third law of thermodynamics
The third law of thermodynamics states that any process consisting of a finite number of stages will not allow it to reach the temperature of absolute zero (although it can be significantly approached).
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 processd 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 part of 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
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.
Second law of thermodynamics
The emergence of the second law of thermodynamics is associated with the need to answer the question of which processes in nature are possible and which are not. The second law of thermodynamics determines the direction of thermodynamic processes.
Using the concept of entropy and Clausius inequality second law of thermodynamics can be formulated as law of increasing entropy closed system with irreversible processes: any irreversible process in a closed system occurs in such a way that the entropy of the system increases.
We can give a more concise formulation of the second law of thermodynamics: in processes occurring in a closed system, entropy does not decrease. It is important here that we are talking about closed systems, since in open systems entropy can behave in any way (decrease, increase, remain constant). In addition, we note again that entropy remains constant in a closed system only during reversible processes. During irreversible processes in a closed system, entropy always increases.
Boltzmann's formula (57.8) allows us to explain the increase in entropy in a closed system during irreversible processes postulated by the second law of thermodynamics: entropy increase means the transition of the system from less likely to more likely condition. Thus, Boltzmann's formula allows us to give a statistical interpretation of the second law of thermodynamics. It, being a statistical law, describes the patterns of chaotic movement of a large number of particles that make up a closed system.
Let us indicate two more formulations of the second law of thermodynamics:
1)according to Kelvin:a circular process is impossible, the only result of which is the transformation of the heat received from the heater into work equivalent to it;
2)according to Clausius:A circular process is impossible, the only result of which is the transfer of heat from a less heated body to a more heated one.
In the middle of the 19th century. there was a problem called heat death of the universe. Considering the Universe as a closed system and applying the second pump of thermodynamics to it, Clausius reduced its content to the statement that the entropy of the Universe must reach its maximum. This means that over time, all forms of motion must turn into thermal motion. The transition of heat from hot bodies to cold ones will lead to the fact that the temperature of all bodies in the Universe will become equal, i.e., complete thermal equilibrium will occur and all processes in the Universe will stop - the thermal death of the Universe will occur. The fallacy of the conclusion about heat death lies in the fact that it makes no sense to apply the second law of thermodynamics to open systems, for example, to such a limitless and endlessly developing system as the Universe.
Entropy, its statistical interpretation and connection with thermodynamic probability
The concept of entropy was introduced in 1865 by R. Clausius. To clarify the physical content of this concept, consider the heat ratio Q, obtained by the body in an isothermal process, to the temperature T heat-releasing body, called given amount of heat.
The reduced amount of heat imparted to the body in an infinitesimal portion of the process is equal to dQ/T. Rigorous theoretical analysis shows that the reduced amount of heat imparted to the body in any reversible circular process, equals zero:
State function, whose differential is dQ/T called entropy and is designated S.
From formula (57.1) it follows that for reversible processes entropy change
(57.3)
In thermodynamics it is proven that the entropy of a system undergoing irreversible cycle increases:
Expressions (57.3) and (57.4) relate only to closed systems, if the system exchanges heat with the external environment, then its entropy can behave in any way. Relations (57.3) and (57.4) can be represented as Clausius inequalities
(57.5)
i.e. entropy of a closed system Maybe or increase(in case of irreversible processes), or remain constant(in the case of reversible processes).
If the system makes an equilibrium transition from the state 1 in a state 2 , then, according to (57.2), the change in entropy
(57.6)
where the integrand and the limits of integration are determined through the quantities characterizing the process under study. Formula (57.6) determines entropy only up to additive constant. It is not entropy itself that has a physical meaning, but the difference in entropies.
Based on expression (57.6), we find the change in entropy in ideal gas processes. So somehow
(57.7)
i.e. the change in entropy D S 1 ® 2 of an ideal gas during its transition from the state 1 in a state 2 does not depend on the type of transition process 1® 2.
So for an adiabatic process dQ = 0, then D S= 0 and therefore S= const, i.e. e. adiabatic reversible process leaks at constant entropy. Therefore it is often called isentropic process. From formula (57.7) it follows that during an isothermal process ( T 1 = T 2)
in an isochoric process ( V 1 = V 2)
Entropy has the property additivity:the entropy of the system is equal to the sum of the entropies of the bodies included in the system. Internal energy, mass, and volume also have the property of additivity (temperature and pressure do not have this property).
The deeper meaning of entropy is revealed in statistical physics: entropy is associated with the thermodynamic probability of the state of the system. Thermodynamic probability W system states are number of ways by which a given state of a macroscopic system can be realized, or the number of microstates that implement a given macrostate (by definition, W³ 1, i.e. thermodynamic probability is not probability in the mathematical sense (the latter £ 1!)).
According to Boltzmann (1872), entropy systems and thermodynamic probability are related to each other as follows:
(57.8)
Where k- Boltzmann's constant. Thus, entropy is determined by the logarithm of the number of microstates with the help of which a given macrostate can be realized. Therefore, entropy can be considered as a measure of probability state of a thermodynamic system. Boltzmann's formula (57.8) 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 that implement a given macrostate, the greater the entropy. In a state of equilibrium - the most probable state of the system - the number of microstates is maximum, and entropy is also maximum.
Since real processes are irreversible, it can be argued that all processes in a closed system lead to an increase in its entropy - 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.
There are several formulations of the second law of thermodynamics, the authors of which are the German physicist, mechanician and mathematician Rudolf Clausius and the British physicist and mechanician William Thomson, Lord Kelvin. Externally they differ, but their essence is the same.
Clausius's postulate
Rudolf Julius Emmanuel Clausius
The second law of thermodynamics, like the first, was also derived experimentally. The author of the first formulation of the second law of thermodynamics is the German physicist, mechanic and mathematician Rudolf Clausius.
« Heat cannot by itself transfer from a cold body to a hot body. " This statement, which Clasius called " thermal axiom”, was formulated in 1850 in the work “On the driving force of heat and on the laws that can be obtained from here for the theory of heat.”“Of course, heat is transferred only from a body with a higher temperature to a body with a lower temperature. In the opposite direction, spontaneous transfer of heat is impossible.” That's the meaning Clausius's postulate , which defines the essence of the second law of thermodynamics.
Reversible and irreversible processes
The first law of thermodynamics shows the quantitative relationship between the heat received by the system, the change in its internal energy and the work done by the system on external bodies. But he does not consider the direction of heat transfer. And it can be assumed that heat can be transferred both from a hot body to a cold one, and vice versa. Meanwhile, in reality this is not so. If two bodies are in contact, then heat is always transferred from the more heated body to the less heated one. Moreover, this process occurs on its own. In this case, no changes occur in the external bodies surrounding the contacting bodies. Such a process that occurs without performing work from the outside (without the intervention of external forces) is called spontaneous . He can be reversible And irreversible.
Spontaneously cooling, a hot body transfers its heat to the colder bodies surrounding it. And a cold body will never naturally become hot. In this case, the thermodynamic system cannot return to its original state. This process is called irreversible . Irreversible processes occur only in one direction. Almost all spontaneous processes in nature are irreversible, just as time is irreversible.
Reversible is a thermodynamic process in which a system passes from one state to another, but can return to its original state by passing through intermediate equilibrium states in reverse order. In this case, all system parameters are restored to their original state. Reversible processes produce the most work. However, in reality they cannot be realized; they can only be approached, since they proceed infinitely slowly. In practice, such a process consists of continuous successive equilibrium states and is called quasi-static. All quasi-static processes are reversible.
Thomson's (Kelvin's) postulate
William Thomson, Lord Kelvin
The most important task of thermodynamics is to obtain the greatest amount of work using heat. Work is easily converted into heat completely without any compensation, for example, through friction. But the reverse process of converting heat into work does not occur completely and is impossible without obtaining additional energy from the outside.
It must be said that the transfer of heat from a colder body to a warmer one is possible. This process occurs, for example, in our home refrigerator. But it cannot be spontaneous. In order for it to flow, it is necessary to have a compressor that will distill such air. That is, for the reverse process (cooling) an external energy supply is required. " It is impossible to transfer heat from a body with a lower temperature without compensation ».
In 1851, another formulation of the second law was given by the British physicist and mechanic William Thomson, Lord Kelvin. Thomson's (Kelvin's) postulate states: “A circular process is impossible, the only result of which would be the production of work by cooling the heat reservoir” . That is, it is impossible to create a cyclically operating engine, the action of which would produce positive work due to its interaction with only one heat source. After all, if this were possible, a heat engine could work using, for example, the energy of the World Ocean and completely converting it into mechanical work. As a result, the ocean would cool due to a decrease in energy. But as soon as its temperature was lower than the ambient temperature, a process of spontaneous transfer of heat from a colder body to a hotter one would have to occur. But such a process is impossible. Consequently, for a heat engine to operate, at least two heat sources are required, having different temperatures.
Perpetual motion machine of the second kind
In heat engines, heat is converted into useful work only when moving from a heated body to a cold one. In order for such an engine to function, a temperature difference is created in it between the heat transmitter (heater) and the heat sink (refrigerator). The heater transfers heat to the working fluid (for example, gas). The working fluid expands and does work. However, not all heat is converted into work. Some of it is transferred to the refrigerator, and some, for example, simply goes into the atmosphere. Then, in order to return the parameters of the working fluid to their original values and start the cycle all over again, the working fluid needs to be heated, that is, heat must be removed from the refrigerator and transferred to the heater. This means that heat needs to be transferred from a cold body to a warmer one. And if this process could be carried out without supplying energy from the outside, we would get a perpetual motion machine of the second kind. But since, according to the second law of thermodynamics, this is impossible to do, it is also impossible to create a perpetual motion machine of the second kind, which would completely convert heat into work.
Equivalent formulations of the second law of thermodynamics:
- A process is impossible, the only result of which is the conversion of the entire amount of heat received by the system into work.
- It is impossible to create a perpetual motion machine of the second kind.
Carnot's principle
Nicolas Leonard Sadi Carnot
But if it is impossible to create a perpetual motion machine, then it is possible to organize the operating cycle of a heat engine in such a way that the efficiency (efficiency factor) is maximum.
In 1824, long before Clausius and Thomson formulated their postulates that defined the second law of thermodynamics, the French physicist and mathematician Nicolas Leonard Sadi Carnot published his work "Reflections on the driving force of fire and on machines capable of developing this force." In thermodynamics it is considered fundamental. The scientist analyzed the steam engines that existed at that time, the efficiency of which was only 2%, and described the operation of an ideal heat engine.
In a water engine, water does work by falling down from a height. By analogy, Carnot suggested that heat can also do work by moving from a hot body to a colder one. This means that in order to The heat engine was working, it must have 2 heat sources having different temperatures. This statement is called Carnot's principle . And the operating cycle of the heat engine created by the scientist was called Carnot cycle .
Carnot came up with an ideal heat engine that could perform the best possible work due to the heat supplied to it.
The heat engine described by Carnot consists of a heater having a temperature T N , working fluid and refrigerator with temperature T X .
The Carnot cycle is a circular reversible process and includes 4 stages - 2 isothermal and 2 adiabatic.
The first stage A→B is isothermal. It takes place at the same temperature of the heater and working fluid T N . During contact the amount of heat Q H transferred from the heater to the working fluid (gas in the cylinder). The gas expands isothermally and performs mechanical work.
In order for the process to be cyclic (continuous), the gas must be returned to its original parameters.
At the second stage of cycle B→C, the working fluid and the heater are separated. The gas continues to expand adiabatically without exchanging heat with the environment. At the same time, its temperature drops to the temperature of the refrigerator T X , and he continues to do work.
At the third stage B→G the working fluid, having a temperature T X , is in contact with the refrigerator. Under the influence of an external force, it is isothermally compressed and releases heat in the amount Q X refrigerator. Work is being done on it.
At the fourth stage G→A, the working fluid will be separated from the refrigerator. Under the influence of an external force, it is compressed adiabatically. Work is being done on it. Its temperature becomes equal to the heater temperature T N .
The working fluid returns to its original state. The circular process ends. A new cycle begins.
The efficiency of a body machine operating according to the Carnot cycle is equal to:
The efficiency of such a machine does not depend on its design. It depends only on the temperature difference between the heater and refrigerator. And if the temperature of the refrigerator is absolute zero, then the efficiency will be 100%. So far no one has been able to come up with anything better.
Unfortunately, in practice it is impossible to build such a machine. Real reversible thermodynamic processes can only approach ideal ones with varying degrees of accuracy. In addition, in a real heat engine there will always be heat losses. Therefore, its efficiency will be lower than that of an ideal heat engine operating according to the Carnot cycle.
Various technical devices have been built based on the Carnot cycle.
If the Carnot cycle is performed in reverse, you get a refrigeration machine. After all, the working fluid will first take heat from the refrigerator, then convert the work spent on creating the cycle into heat, and then give this heat to the heater. Refrigerators work on this principle.
The reverse Carnot cycle is also the basis of heat pumps. Such pumps transfer energy from sources with a low temperature to a consumer with a higher temperature. But, unlike a refrigerator, in which the extracted heat is released into the environment, in a heat pump it is transferred to the consumer.