The first law of thermodynamics is one of the three basic laws of thermodynamics, which is the law of conservation of energy for systems in which thermal processes are essential.
According to the first law of thermodynamics, a thermodynamic system (for example, steam in a heat engine) can do work only due to its internal energy or any external energy sources.
The first law of thermodynamics explains the impossibility of the existence of a perpetual motion machine of the 1st kind, which would do work without drawing energy from any source.
The essence of the first law of thermodynamics is as follows:
When a thermodynamic system is informed of a certain amount of heat Q, in the general case, the internal energy of the system DU changes and the system performs work A:
Equation (4), expressing the first law of thermodynamics, is the definition of the change in the internal energy of the system (DU), since Q and A are independently measurable quantities.
The internal energy of the system U can, in particular, be found by measuring the work of the system in an adiabatic process (that is, at Q \u003d 0): And hell \u003d - DU, which determines U up to some additive constant U 0:
U = U + U 0 (5)
The first law of thermodynamics states that U is a function of the state of the system, that is, each state of a thermodynamic system is characterized by a certain value of U, regardless of how the system is brought to this state (while the values of Q and A depend on the process that led to the change system state). When studying the thermodynamic properties of physical systems, the first law of thermodynamics is usually used in conjunction with the second law of thermodynamics.
3. The second law of thermodynamics
The second law of thermodynamics is the law according to which macroscopic processes proceeding at a finite rate are irreversible.
Unlike ideal (lossless) mechanical or electrodynamic reversible processes, real processes associated with heat transfer at a finite temperature difference (i.e., flowing at a finite speed) are accompanied by various losses: friction, gas diffusion, expansion of gases into a void, release of Joule heat, etc.
Therefore, these processes are irreversible, that is, they can spontaneously proceed in only one direction.
The second law of thermodynamics arose historically in the analysis of the operation of heat engines.
The very name "The Second Law of Thermodynamics" and its first formulation (1850) belong to R. Clausius: "... a process is impossible in which heat would transfer spontaneously from colder bodies to hotter bodies."
Moreover, such a process is impossible in principle: neither by direct transfer of heat from colder bodies to warmer ones, nor by means of any devices without the use of any other processes.
In 1851, the English physicist W. Thomson gave a different formulation of the second law of thermodynamics: “Processes are impossible in nature, the only consequence of which would be the lifting of a load produced by cooling a thermal reservoir.”
As you can see, both of the above formulations of the second law of thermodynamics are almost the same.
This implies the impossibility of implementing an engine of the 2nd kind, i.e. engine without energy losses due to friction and other associated losses.
In addition, it follows from this that all real processes occurring in the material world in open systems are irreversible.
In modern thermodynamics, the second law of thermodynamics of isolated systems is formulated in a single and most general way as the law of increase in a special function of the state of the system, which Clausius called entropy (S).
The physical meaning of entropy is that in the case when the material system is in complete thermodynamic equilibrium, elementary particles, of which this system consists, are in an uncontrolled state and perform various random chaotic movements. In principle, one can determine the total number of these possible states. The parameter that characterizes the total number of these states is entropy.
Let's look at this with a simple example.
Let an isolated system consist of two bodies "1" and "2" with different temperatures T 1 >T 2 . Body "1" gives off a certain amount of heat Q, and body "2" receives it. In this case, there is a heat flow from the body "1" to the body "2". As the temperatures equalize, the total number of elementary particles of bodies "1" and "2", which are in thermal equilibrium, increases. As this number of particles increases, so does the entropy. And as soon as the complete thermal equilibrium of bodies "1" and "2" comes, the entropy will reach its maximum value.
Thus, in a closed system, the entropy S either increases or remains unchanged for any real process, i.e., the change in entropy dS ³ 0. The equal sign in this formula takes place only for reversible processes. In a state of equilibrium, when the entropy of a closed system reaches its maximum, no macroscopic processes in such a system, according to the second law of thermodynamics, are possible.
It follows that entropy is a physical quantity that quantitatively characterizes the features of the molecular structure of a system, on which the energy transformations in it depend.
The relationship of entropy with the molecular structure of the system was first explained by L. Boltzmann in 1887. He established the statistical meaning of entropy (formula 1.6). According to Boltzmann (high order has a relatively low probability)
where k is the Boltzmann constant, P is the statistical weight.
k = 1.37 10 -23 J/K.
The statistical weight P is proportional to the number of possible microscopic states of the elements of a macroscopic system (for example, different distributions of coordinates and momenta of gas molecules corresponding to a certain value of energy, pressure, and other thermodynamic parameters of the gas), i.e., it characterizes a possible discrepancy between the microscopic description of a macrostate.
For an isolated system, the thermodynamic probability W of a given macrostate is proportional to its statistical weight and is determined by the entropy of the system:
W = exp(S/k). (7)
Thus, the law of entropy increase has a statistically probabilistic nature and expresses the constant tendency of the system to transition to a more probable state. It follows from this that the most probable state achievable for the system is one in which events occurring simultaneously in the system are statistically mutually compensated.
The maximum probable state of the macrosystem is the state of equilibrium, which it can, in principle, reach in a sufficiently long period of time.
As mentioned above, entropy is an additive quantity, that is, it is proportional to the number of particles in the system. Therefore, for systems with a large number particles, even the most insignificant relative change in the entropy per particle significantly changes its absolute value; a change in the entropy, which is in the exponent in equation (7), leads to a change in the probability of a given macrostate W by a huge number of times.
It is this fact that is the reason why, for a system with a large number of particles, the consequences of the second law of thermodynamics are practically not probabilistic, but reliable. Extremely unlikely processes, accompanied by any noticeable decrease in entropy, require such huge waiting times that their implementation is practically impossible. At the same time, small parts of the system containing a small number of particles experience continuous fluctuations accompanied by only a small absolute change in entropy. The average values of the frequency and size of these fluctuations are as reliable a consequence of statistical thermodynamics as the second law of thermodynamics itself.
The literal application of the second law of thermodynamics to the Universe as a whole, which led Clausius to the wrong conclusion about the inevitability of the "thermal death of the Universe", is illegal, since in principle absolutely isolated systems cannot exist in nature. As will be shown below, in the section of non-equilibrium thermodynamics, the processes occurring in open systems obey other laws and have other properties.
The internal energy can change mainly due to two different processes: performing work A on the body and imparting to it the amount of heat Q. The performance of work is accompanied by the movement of external bodies acting on the system. So, for example, when a piston closing a vessel with gas is pushed in, the piston, moving, does work L on the gas. According to the third law. Newton's gas does work on the piston
The communication of heat to the gas is not associated with the movement of external bodies and, therefore, is not associated with the performance of macroscopic work on the gas (that is, related to the entire set of molecules that make up the body) work. In this case, the change in internal energy is due to the fact that individual molecules of a more heated body do work on individual molecules of a body that is less heated. The transfer of energy also takes place via radiation. The totality of microscopic (that is, not capturing the whole body, but its individual molecules) processes leading to the transfer of energy from body to body is called heat transfer.
Just as the amount of energy transferred from one body to another is determined by the work A performed on each other by bodies, the amount of energy transferred from body to body by heat transfer is determined by the amount of heat Q given by one body to another. Thus, the increment in the internal energy of the system must be equal to the sum of the work done on the system A and the amount of heat imparted to the system
Here are the initial and final values of the internal energy of the system. Usually, instead of the work A performed by external bodies on the system, one considers the work A (equal to -A) performed by the system on external bodies. Substituting -A for A and solving equation (83.1) for Q, we get:
Equation (83.2) expresses the law of conservation of energy and is the content of the first law (beginning) of thermodynamics. It can be expressed in words as follows: the amount of heat communicated to the system goes to increase the internal energy of the system and to perform work on external bodies by the system.
The foregoing does not mean at all that the internal energy of the system always increases with the addition of heat. It may happen that, despite the communication of heat to the system, its energy does not increase, but decreases. In this case, according to (83.2), i.e., the system does work both due to the received heat Q and due to the internal energy reserve, the loss of which is equal to . It must also be borne in mind that the quantities Q and A in (83.2) are algebraic, which means that the system does not actually receive heat, but gives it away).
From (83.2) it follows that the amount of heat Q can be measured in the same units as work or energy. The SI unit for heat is the joule.
It is also used to measure the amount of heat special unit called a calorie. One calorie is equal to the amount of heat required to heat 1 g of water from 19.5 to 20.5 °C. A thousand calories is called a big calorie or kilocalorie.
It has been experimentally established that one calorie is equivalent to 4.18 J. Therefore, one joule is equivalent to 0.24 cal. The value is called the mechanical equivalent of heat.
If the quantities included in (83.2) are expressed in different units, then some of these quantities must be multiplied by the corresponding equivalent. So, for example, expressing Q in calories, and U and A in joules, relation (83.2) should be written as
In what follows, we will always assume that Q, A, and U are expressed in the same units, and write the equation of the first law of thermodynamics in the form (83.2).
When calculating the work done by the system or the heat received by the system, it is usually necessary to break the process under consideration into a number of elementary processes, each of which corresponds to a very small (in the limit, infinitely small) change in the system parameters. Equation (83.2) for an elementary process has the form
where is the elementary amount of heat, is the elementary work, and is the increase in the internal energy of the system during this elementary process.
It is very important to keep in mind that and cannot be considered as increments of Q and A.
Any value corresponding to the elementary process A can be considered as an increment of this value only if the value corresponding to the transition from one state to another does not depend on the path along which the transition occurs, i.e., if the value f is a function of the state. With regard to the state function, we can talk about its "reserve" in each of the states. For example, we can talk about the stock of internal energy that a system has in various states.
As we will see later, the amount of work done by the system and the amount of heat received by the system depend on the path of the system's transition from one state to another. Therefore, neither Q nor A are state functions, so one cannot talk about the amount of heat or work that the system has in different states.
The thermodynamic process is called reversible if it can occur both in the forward and in the opposite direction, and if such a process occurs first in the forward and then in the opposite direction and the system returns to its original state, then no changes occur in the environment and in this system.
Any process that does not satisfy these conditions is irreversible.
Any equilibrium process is reversible. The reversibility of the equilibrium process occurring in the system follows from the fact that its any intermediate state is a state of thermodynamic equilibrium; whether the process is forward or reverse. Real processes are accompanied by energy dissipation (due to friction, heat conduction, etc.), which is not considered by us. Reversible processes are idealizations of real processes. Their consideration is important for the 2nd reasons: 1) many processes in nature and technology are practically reversible; 2) reversible processes are the most economical; have the maximum thermal efficiency, which allows us to indicate ways to increase the efficiency of real heat engines.
The work done by a gas when its volume changes.
Work is done only when the volume changes.
Let us find in general terms the external work done by the gas when its volume changes. Consider, for example, a gas under a piston in a cylindrical vessel. If the expanding gas moves the piston to an infinitesimal distance dl, then it does work on it
A=Fdl=pSdl=pdV, where S is the area of the piston, Sdl=dV is the change in system volume. Thus, A= pdV.(1)
The total work A performed by the gas when its volume changes from V1 to V2 is found by integrating formula (1): A= pdV(from V1 to V2).(2)
The integration result is determined by the nature of the relationship between pressure and gas volume. The expression (2) found for work is valid for any changes in the volume of solid, liquid and gaseous bodies.
P
The total work done by the gas will be figure area, limited by the abscissa axis, the curve and the values V1, V2.
Graphically, only equilibrium processes can be depicted - processes consisting of a sequence of equilibrium states. They proceed in such a way that the change in thermodynamic parameters over a finite period of time is infinitely small. All real processes are nonequilibrium (they proceed at a finite rate), but in some cases their nonequilibrium can be neglected (the slower the process proceeds, the closer it is to equilibrium).
First law of thermodynamics.
There are 2 ways to exchange energy between bodies:
transfer of energy through heat transfer (through heat transfer);
through doing work.
Thus, we can talk about 2 forms of energy transfer from one body to another: work and heat. The energy of mechanical motion can be converted into the energy of thermal motion, and vice versa. During these transformations, the law of conservation and transformation of energy is observed; as applied to thermodynamic processes, this law is the first law of thermodynamics:
∆U=Q-A or Q=∆U+A .(1)
That is, the heat imparted to the system is spent on changing its internal energy and on doing work against external forces. This expression in differential form will look like Q=dU+A (2) , where dU is an infinitesimal change in the internal energy of the system, A is elementary work, Q is an infinitesimal amount of heat.
It follows from formula (1) that in SI the amount of heat is expressed in the same units as work and energy, i.e. in joules (J).
If the system periodically returns to its original state, then the change in its internal energy is ∆U=0. Then, according to the 1st law of thermodynamics, A=Q,
That is, a perpetual motion machine of the first kind - a periodically operating engine that would do more work than the energy communicated to it from the outside - is impossible (one of the formulations of the 1st law of thermodynamics).
Application of the 1st law of thermodynamics to isoprocesses and to an adiabatic process.
Among the equilibrium processes occurring with thermodynamic systems, isoprocesses stand out, in which one of the main state parameters remains constant.
Isochoric process (V= const)
In such a process, the gas does not perform work on external bodies, i.e. A=pdV=0.
Then, from the 1st law of thermodynamics, it follows that all the heat transferred to the body goes to increase its internal energy: Q=dU. Knowing that dU m =C v dT.
Then for an arbitrary mass of gas we obtain Q= dU=m\M* C v dT.
Isobaric process (p= const).
In this process, the work of the gas with an increase in volume from V1 to V2 is equal to A= pdV(from V1 to V2)=p(V2-V1) and is determined by the area of the figure bounded by the abscissa axis, the curve p=f(V) and the values of V1, V2. If we recall the Mendeleev-Clapeyron equation for the 2 states we have chosen, then
pV 1 =m\M*RT 1 , pV 2 =m\M*RT 2 , whence V 1 - V 2 = m\M*R\p(T 2 - T 1). Then the expression for the work of the isobaric expansion will take the form A= m\M*R(T 2 - T 1) (1.1).
In an isobaric process, when a gas of mass m is informed of the amount of heat
Q=m\M*C p dT its internal energy increases by dU=m\M*C v dT. In this case, the gas performs work determined by the expression (1.1).
Isothermal process (T= const).
This process is described by the Boyle-Mariotte law: pV=const.
Let's find the work of isothermal gas expansion: A= pdV(from V1 to V2)= m/M*RTln(V2/V1)=m/M*RTln(p1/p2).
Since at Т=const the internal energy of an ideal gas does not change: dU=m/M* C v dT=0, then from the 1st law of thermodynamics (Q=dU+A) it follows that for an isothermal process Q= A, i.e. the entire amount of heat imparted to the gas is spent on doing work against external forces: Q=A=m/M*RTln(p1/p2)=m/M*RTln(V2
Therefore, in order for the temperature not to decrease during the expansion of the gas, it is necessary to supply the gas with an amount of heat during the isothermal process that is equivalent to the external work of expansion.
Application of the first law of thermodynamics to the isoprocesses of an ideal gas. The dependence of the heat capacity of an ideal gas on the type of process. Mayer formula.
The work done by the gas during isoprocesses.
adiabatic process. polytropic processes.
Basic thermodynamic concepts: internal energy, work, heat. Equation of the first law of thermodynamics.
Basic thermodynamic concepts
Internal energy– energy physical system, depending on her internal state. Internal energy includes energy chaotic (thermal) motion all microparticles of the system (molecules, atoms, ions, etc.) and the interaction energy of these particles. Kinetic energy of motion of the system as a whole and its potential energy in external force fields does not enter into internal energy. In thermodynamics and its applications it is of interest not the meaning internal energy and its change when the state of the system changes. Internal energy is a function of the state of the system.
Work thermodynamic system over external bodies is in changing the state of these bodies and is determined by the amount of energy transferred by the system to external bodies when the volume changes.
Force created by gas pressure 
on piston square 
is equal to 
. Work done when moving the piston 
, is equal to 
, where 
change in gas volume (Fig. 14.1), that is
 |
Heat(quantity of heat) - the amount of energy received or given off by the system during heat exchange. Elementary amount of heat
is not generally a differential any state parameter function. The amount of heat transferred to the system, like work, depends on how does the system go from the initial state to the final. (In contrast to the internal energy, for which 
, but 
, one cannot say how much work the body contains, “this is a function” of the process - a dynamic characteristic). 1st law (beginning) of thermodynamics: the amount of heat communicated to the system goes to increase the internal energy of the system and to perform work on external bodies by the system.
 |
where
the amount of heat imparted to the body; 
And 
initial and final values of internal energy;
work done by the system on external bodies.
In differential form, 1st beginning:
 |
the elementary amount of heat communicated to the body; 
change in internal energy;
the work done by the body (for example, the work done when the gas expands).
Application of the 1st law of thermodynamics to ideal gas isoprocesses
(Greek) - equal). Processes occurring at some constant parameter ( 
isothermal; 
isobaric; 
isochoric). heat capacity 
body is called a value equal to the ratio of the amount of heat communicated to the body 
to the corresponding temperature increment 
.
 |
The dimension of the heat capacity of the body
.
Similar definitions are introduced for 1 mole (molar heat capacity
), and for a unit mass of a substance 
.
Consider heating a gas at constant volume. According to the first law of thermodynamics:
, then 
.
by definition, but for a process with :
, where
heat capacity of a gas at constant volume.
Then 
And
 |
Heat capacity of gas at constant pressure:
.
For an ideal gas for 1 mole (from the Mendeleev-Clapeyron equation).
.
Differentiate this expression with respect to temperature T, we get:
, we get for 1 mole
 |
But the expression is called Mayer equation. It shows that
always more 
by the value of the molar gas constant. This is explained by when gas is heated at constant pressure compared to a process at constant volume, an additional amount of heat is required to perform the work of expansion of the gas, because the constancy of pressure is ensured by increasing the volume of gas.
At adiabatic process(process proceeding without heat exchange with the external environment).
, 
, i.e. the heat capacity in an adiabatic process is zero. 
There are processes in which expanding gas does work greater than the received heat, then it the temperature drops despite the heat input. Heat capacity in this case negative. In general
.
3. The work done by the gas during isoprocesses
isobaric 
.
 |
Diagram of this process (isobars) in coordinates  depicted as a straight line parallel to the axis  (Fig. 14.2). In an isobaric process, the work done by a gas as the volume expands from  before  is equal to:
|
|
|
Rice. 14.2 |
And it is determined by the area of the shaded rectangle in Fig. 14.2.
Isochoric process(). Diagram of this process
 |
(isochore) in coordinates is depicted as a straight line parallel to the y-axis (Fig. 14.3). because , then  .
Isothermal process(). (Fig. 14.4). Using the Mendeleev-Claiperon equation of state for an ideal gas to work in an isothermal process, we obtain: |
||
|
Rice. 14.3 |
|||
 | |||
Isothermal process is perfect process, because expansion of a gas at constant temperature can only occur infinitely slow. At a finite expansion rate, temperature gradients will occur.
4. Adiabatic (adiabatic) process
This is a process that occurs without heat exchange with the surrounding bodies.. Let us consider under what conditions it is possible to actually carry out an adiabatic process, or approach it.
1. Required adiabatic shell, whose thermal conductivity is zero. An approximation to such a shell can be Dewar vessel.
2. 2nd case - very fast processes. The heat does not have time to spread and for some time it can be assumed.
3. Processes running in very large volumes of gas, for example, in the atmosphere (regions of cyclones, anticyclones). To equalize the temperature, heat transfer must occur from neighboring, more heated layers of air, which often takes a considerable time.
For an adiabatic process, the first law of thermodynamics:
or 
.
In case of gas expansion 
, 
, (temperature will drop). If the gas is compressed 
, then 
(temperature rises). Let us derive an equation relating the gas parameters in an adiabatic process. We take into account that for an ideal gas 
, then
Divide both sides of the equation by 
:
.
From Mayer's equation 
, then
.
Denote 
.
.
Let's integrate this equation:
 |
From here
Received Poisson's equation(for adiabatic) (1st form). Let's replace 
:
,
2nd form Poisson equations. On fig. 14.5 presents comparative graphs of isotherms and adiabats.
Rice. 14.5
Because
, then the adiabatic curve is steeper than the isotherm. Compute work in an adiabatic process:
those
Polytropic processes.
This is the name of processes whose equation in variables 
has the form
where n is an arbitrary number, both positive and negative, and also equal to zero. The corresponding curve is called polytropic. Polytropic processes are, in particular, adiabatic, isothermal, isobaric, isochoric.
Questions for self-control
Lecture #15
Second law of thermodynamics
Plan
Reversible and irreversible processes. Circular process (cycle). Equilibrium states and processes.
. Maximum efficiency of thermal motion.
Heat engines and refrigeration machines.
Entropy. Entropy increase law.
Statistical weight (thermodynamic probability). The second law of thermodynamics and its statistical interpretation.
1. Reversible and irreversible processes
Let, as a result of some process in an isolated system, the body passes from the state BUT into a state IN and then returns to the initial state BUT. The process is called reversible, if it is possible to make the reverse transition from IN in BUT through the same intermediate states as in the direct process, to no change left both in the body itself and in the surrounding bodies. If the reverse process is impossible, or at the end of the process in the surrounding bodies and in the body itself, any changes remain, then the process is irreversible.
Examples of irreversible processes. Any process accompanied friction is irreversible (the heat released during friction cannot be collected and again turned into work without the expenditure of work of another body). All processes accompanied by heat transfer from a heated body to a less heated one are irreversible(for example, thermal conductivity). Irreversible processes also include diffusion, viscous flow. All irreversible processes are nonequilibrium.
equilibrium are processes that are sequence of equilibrium states. equilibrium state- this is a state in which, without external influences, the body can be arbitrarily long. (Strictly speaking, an equilibrium process can only be infinitely slow. Any real processes in nature proceed at a finite rate and are accompanied by energy dissipation. Reversible processes - idealization when irreversible processes can be neglected).
Circular process (cycle). If the body is out of state BUT into a state IN passes through some intermediate states, and returns to the initial state BUT through other intermediate states, then circular process, or cycle.
The circular process is reversible if all its parts reversible. If any part of the cycle is irreversible, then the whole process is irreversible.
2. Carnot cycle and its efficiency for an ideal gas
(Sadie Carnot (1796 - 1832) - French physicist).
 |
The Carnot cycle is as follows. First, the system, having a temperature  , is given in thermal contact with the heater. Then, infinitely slowly reducing the external pressure, it is forced to expand along isotherm 1-2. And she gets warm.  from the heater and produces work  against external pressure.
|
– refrigerator(or heat receiver). The reservoirs are so large that giving or receiving heat does not change their temperature. After that, the system is adiabatically isolated and forced expand along the adiabatic 2 – 3 until its temperature reaches the temperature of the refrigerator. At adiabatic expansion the system also does some work against external pressure. In state 3, the system is brought to thermal contact with the refrigerator and continuous an increase in pressure isothermally compresses it up to some state 4. Moreover, over the system work is done (i.e. the system itself does negative work 
), and it gives the refrigerator some The amount of heat 
. State 4 selectable so that it would be possible to return the system to its original state by compression along the adiabatic 4 – 1. To do this, work must be done on the system 
(the system must produce negative work 
). As a result of the circular Carnot process the internal energy of the system does not change, so the work done 
Calculate efficiency of an ideal heat engine operating on the Carnot cycle. This value is relation amount of heat turned into work, to the amount of heat received from the heater.
 |
Useful work per cycle is equal to the sum of all the work of the individual parts of the cycle:
Work of isothermal expansion:
,
adiabatic expansion:
,
isothermal compression:
,
adiabatic compression:
Adiabatic sections cycle do not affect on the overall result, because work on them equal and opposite sign, therefore 
.
. (1)
Since the gas states described by points 2 and 3 lie on the same adiabat, the gas parameters are related by the Poisson equation:
.
Similarly for points 4 and 1:
Dividing these equations term by term, we get:
, then from (1) it turns out
 |
That is, the efficiency of the Carnot cycle is determined only by the temperatures of the heater and refrigerator.
Carnot's theorem(no proof): The efficiency of all reversible machines operating at the same temperatures of the heater and cooler is the same and is determined only by the temperatures of the heater and cooler..
Comment: efficiency of real heat engine always below than the efficiency of an ideal heat engine (in a real engine, there are heat loss, which are not taken into account when considering an ideal machine).
3. The principle of operation of a heat engine and a refrigeration machine
Any heat engine is from 3 main parts: working fluid, heater and cooler.
The working fluid receives a certain amount of heat from the heater. When compressed, the gas transfers some heat to the refrigerator. Received work performed by the engine per cycle:
(Note: real heat engines usually operate according to the so-called open loop when the gas after expansion thrown out, And compresses a new portion. However, this does not significantly affect the thermodynamics of the process. IN closed cycle expands and contracts the same portion.).
Refrigeration machine. The Carnot cycle is reversible, so it can be done in the opposite direction. (4-3-2-1-4 (fig.15.3)) From the refrigerator compartment absorbs heat .
 |
heater the working fluid transfers a certain amount warmth  . External forces do work  , then
As a result of the cycle some heat is transferred from a cold body to a body with a higher temperature. Really the working fluid in a refrigeration plant is usually vapors of low-boiling liquids- ammonia, freon, etc. Energy is supplied to the machine from |
|
Rice. 15.3 |
electrical network. Due to this energy, the process “ heat transfer” from the refrigerator compartment to hotter bodies (to the environment).
Refrigeration plant efficiency estimated by the coefficient of performance:
 |
Heat pump. This is a continuously operating machine, which, due to the expenditure of work 
(electricity) takes away heat from a source with a low temperature (most often close to to temperature environment
) and transfers it to a heat source with a higher temperature 
the amount of heat is equal to sum heat taken from a low-temperature source and work expended: 
.
always greater than one (the maximum possible 
).
For comparison: if you heat the room with conventional electric heaters, then quantity of heat, allocated in the heating elements, exactly equal to electricity consumption.
4 . Entropy. Entropy Increasing Law
In thermodynamics, the concept of “entropy” was introduced by the German physicist R. Clausius (1865).
From static physics: the ratio of the amount of heat 
reported to the system to the temperature 
(system) is an increment of some state function(entropy).
Each state of the body is characterized by a certain value of entropy. If we denote the entropy in states 1 and 2 as 
And 
, then by definition for reversible processes:
 |
The value of an arbitrary constant with which entropy is defined does not matter. It is not the entropy itself that has physical meaning, but the difference between the entropies.
Entropy Increasing Law.
Assume that an isolated system goes from equilibrium
 |
(for the reverse process, the sign “=” , for the irreversible “For our transition 1 - 2 - 1:
.
Since the process 2 - 1 is reversible, there will be equality. ( Entropy Increasing Law).
5. Statistical weight (thermodynamic probability).
Under thermodynamic probability understood number of microstates(microdistributions, for example, distributions of molecules in space or energy) which can determine the considered macro distribution.
3rd and 4th - in the first, etc. (Fig. 15.5).
|
, |
const),
where 
Boltzmann constant, 
thermodynamic probability.
The second law of thermodynamics and its statistical interpretation
Boltzmann's formulation:
Clausius' formulation:
.
, then 
This means that for every 
transition cases 
from a body with a temperature of 301 K to a body with a temperature of 300 K, one case of the transition of the same amount of heat from a body with a temperature of 300 K to a body with a temperature of 301 K can occur. (Note that for a very small amount of heat 
the probabilities become comparable and for such cases the second law can no longer be applied.).
In general, speaking if there is a multivariance of paths, processes in the system, then, having calculated the entropy of the final states, one can theoretically determine the probability of one or another path, process, without actually producing them, and this is important practical use formula relating thermodynamic probability to entropy.
Questions for self-control
REFERENCES
1.Irodov I.E. Physics of macrosystems. - M. - S. - Pb.: Fizmatlit,
2. Saveliev I.V.. Course of General Physics: In 3 vols. - M .: Nauka, 1977. Vol. 1. - 432s.
3.Matveev A.N. Molecular physics. - M .: Higher. Shk., 1987.
4.Sivukhin D.V. General course of physics: In 5 volumes. - M.: Nauka, 1975. v.2.
5.Telesnin R.V.. Molecular physics. - M .: Higher. school, 1973. -
6.Zisman G.A., Todes O.M. General physics course: In 3 volumes. – M.:
Nauka., 1969. T 1. - 340s.
7.Trofimova T.I. Physics course. - M .: Higher. school, 1990. - 478s.
8.Kunin V.N.. Lecture notes on difficult sections of physics
Vladim. polytechnic in-t. - Vladimir, 1982 / - 52s.
9. Physics. Program, guidelines and tasks for
correspondence students (with examples of solutions) / Comp.: A.F. Gal-
kin, A.A. Kulish, V.N. Kunin and others; Ed. A.A. Kulish; Vla-
dim. state un-t. - Vladimir, 2002. - 128s.
10. Guidelines for independent work in fi
zike / Comp.: E.V. Orlik, E.D. Korzh, V.G. Prokoshev; Vladim.
state un-t. - Vladimir, 1988. - 48s.
Lecture number 7. molecular kinetic theory
ideal gas…………………………………………………….4
Lecture No. 8. elements of classical statistics
(statistical physics)…………………………………………………12
Lecture number 9. real gases……………………………………………………..25
Lecture number 10. properties of liquids………………………………………….32
Lecture number 11. properties of solids…………………………………….......40
Lecture number 12. phase equilibria and phase transitions………….47
One of characteristic features The thermodynamic consideration of phenomena consists in isolating one body from a multitude of bodies that are in interaction, which is called the system under study, while the rest of the bodies are called the external environment or external bodies. In this method, all attention is paid to the selected system, its geometric boundaries are often chosen to be conditional and such that they are convenient for solving the problem under consideration. The system is assumed to be at rest, so the energy changes in it are completely reduced to a change in its internal energy. Interaction with external bodies is established in the most general form: energy can be transferred between the system and external bodies in the form of heat and work.
Figure 2.5 schematically shows the system under study and external bodies II and III. The system is placed in a cylinder with a bottom and a movable piston A A. Let the walls and piston of the cylinder be adiabatic, and the bottom of the cylinder be heat-permeable. Then, obviously, the selected system I is in thermal contact with body II (heat exchange is possible with this body), while with body III it is in mechanical contact (energy exchange is possible with this body through the work done when the piston moves). The arrows in the figure show that an elementary amount of heat enters the system from body II, while the system, performing elementary work on body III, transfers energy to it. As a result, there is a change
internal energy of the system According to the diagram shown in Figure 2.5,
The written equation expresses the first law of thermodynamics: the amount of heat received by the system from surrounding bodies goes to change its internal energy and to perform work on external bodies.
It must be borne in mind that the quantities are algebraic, it is generally accepted that if the system receives this heat, and if the system does work on external bodies, transferring energy to them. When interpreting equation (17.1), for simplicity, it was said that this received heat is perfect work. But in the general case, a body can give off heat, then either receive energy through work
In a system enclosed in an adiabatic shell, the processes are not accompanied by heat exchange with the surrounding bodies; such processes are called adiabatic. For adiabatic processes and according to The last expression means the following: work in the adiabatic process occurs due to the loss of internal energy. If (external bodies do work on the system), then (the internal energy of the system increases).
If the shell of the system is rigid (mechanical isolation), then the mechanical work with any changes in the system is equal to zero. Such processes are called isochoric (isochoric), for them Thus, with isochoric changes in the system, its internal energy changes only due to the input or output heat.
One more feature of equation (17.1) should be noted: there is a differential of the internal energy of the body under study, while the quantities are elementary (small) values of heat and work; (see Fig. 2.5) - the elementary amount of heat transferred from body II to body work of body I on body III. In this case, body II can exchange energy with a number of other bodies, which is why, in the general case, it cannot be the energy differential of the second body. For the system under study, there is a part and therefore also cannot be the total differential of any state function of the system under study. The elementary work that determines the exchange of energy between the system and the third body is not a complete differential either.
When determining the final change in the state of the system, due to its transition from state 1 to state 2, the expression
(17.1) integrate over the transition line or, which is the same:
The last equality expresses the first law of thermodynamics for the final changes in the system. According to the above, these are the final values of heat and work (but not an increment of something), while the value is an increment of internal energy.
As mentioned earlier (§ 16, 13), it does not depend, but depends on the type of process (on the path of the system's transition from the initial state to the final one). In this regard, it follows from equation (17.2) that it also depends on the type of process.
If, when the state of the system changes, its temperature changes by then, dividing (17.2) by we get:
Ratio - determines the heat capacity of the system. Transitions between two states can occur in such a way that the temperature change is the same, but the values for different transitions will be different (for different jobs). It follows that the heat capacity of system (17.3) will also depend on the type of process.