The first law of thermodynamics is written as First law of thermodynamics. Internal energy, warmth. The work of a gas during expansion. Examples of problem solving

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, the elementary particles that make up this system 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 character 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 of particles, even the smallest 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.

To measure the amount of heat, a special unit called a calorie is also used. 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.

Internal energy U A thermodynamic system can be changed in two ways: by performing mechanical work and by heat transfer. If both methods are used at the same time, then we can write

\(~\Delta U = Q - A \) or \(~Q = \Delta U + A .\)

This formula expresses first law of thermodynamics.

• The amount of heat imparted to a thermodynamic system is spent on changing its internal energy and on doing work by the system against external forces.

If instead of work A systems over external bodies introduce the work of external forces A " (BUT = –A"), then the first law of thermodynamics can be rewritten as follows:

\(~\Delta U = Q + A" .\)

• The change in the internal energy of a thermodynamic system is equal to the sum of the work done on the system by external forces and the amount of heat transferred to the system in the process of heat transfer.

The first law of thermodynamics is a generalization of the law of conservation of energy for mechanical and thermal processes. For example, consider the process of braking a bar on a horizontal surface under the action of a friction force. The speed of the bar decreases, the mechanical energy "disappears". But at the same time, the rubbing surfaces (bar and horizontal surface) heat up, i.e. mechanical energy is converted into internal energy.

Application of the first law to various thermal processes

Isochoric process

The volume does not change: V= const. Therefore, Δ V= 0 and BUT = –A" = 0, i.e. no mechanical work is done. The first law of thermodynamics will look like:

\(~Q = \Delta U.\)

• In an isochoric process, all the energy supplied to the gas by heat exchange is spent entirely on increasing its internal energy.

Isothermal process

The gas temperature does not change: Τ = const. Therefore, Δ T= 0 and ∆ U= 0. The first law of thermodynamics will have the form:

\(~Q = A.\)

• In an isothermal process, all the energy imparted to the gas by heat transfer goes to the gas doing work.

isobaric process

Pressure does not change: p= const. As the gas expands, work is done Α = p⋅Δ V and heats up, i.e. its internal energy changes.

The first law of thermodynamics will be:

\(~Q = A + \Delta U .\)

• In an isobaric process, the amount of heat imparted to a thermodynamic system is spent on changing its internal energy and on doing work by the system against external forces.

adiabatic process

adiabatic process- this is a process that occurs without heat exchange between the system and the environment, i.e. Q = 0.

Such processes occur with good thermal insulation of the system or with fast processes, when heat exchange practically does not have time to occur. The first law of thermodynamics will be:

\(~\Delta U + A = 0\) or \(A = -\Delta U .\)

If BUT > 0 (Δ V> 0 the gas expands), then Δ U < 0 (газ охлаждается), т.е.

• During adiabatic expansion, the gas does work and cools itself.

Cooling air during adiabatic expansion causes, for example, the formation of clouds.

If BUT < 0 (ΔV < 0 газ сжимается), то ΔU> 0 (gas heats up), i.e.

• Under adiabatic compression, work is done on the gas and the gas heats up.

This is used, for example, in diesel engines, where, when the air is compressed rapidly, the temperature rises so much that the fuel vapors in the engine ignite.

The adiabatic change in the state of a gas can be expressed graphically. The schedule for this process is called adiabatic. For the same initial conditions ( p 0 , V 0) during adiabatic expansion, the gas pressure decreases faster than during isothermal expansion (Fig. 1), since the pressure drop is caused not only by an increase in volume (as in isothermal expansion), but also by a decrease in temperature. Therefore, the adiabat goes below the isotherm and the gas does less work during adiabatic expansion than during isothermal expansion.

From the first law of thermodynamics follows the impossibility of creating perpetual motion machine of the first kind, i.e. such an engine that would do work without the expenditure of energy from the outside.

Indeed, if no energy is supplied to the system ( Q= 0), then A = –Δ U and work can be done only at the expense of the loss of internal energy of the system. After the energy supply is exhausted, the engine will stop working.

see also

1. Are you familiar with the perpetual motion machine? // Quantum. - 2003. - No. 3. - C. 32-33
2. Mogilevsky M. Leonardo da Vinci and the impossibility principle of a perpetual motion machine // Kvant. - 1999. - No. 5. - S. 14-18

Heat balance equation

If the system is closed (the work of external forces A" = 0) and thermally insulated ( Q= 0), then the first law of thermodynamics will look like:

\(~\Delta U = 0 .\)

If there are bodies with different temperatures in such a system, then heat exchange will occur between them: bodies with a higher temperature will give off energy and cool, and bodies with a lower temperature will receive energy and heat up. This will happen until the temperatures of all bodies become the same, i.e. a state of thermodynamic equilibrium occurs. Wherein

\(~Q_1 + Q_2 + \ldots + Q_n = 0 .\)

The first law of thermodynamics for a closed and adiabatically isolated system is called heat balance equation but:

• in a closed system of bodies, the algebraic sum of the amounts of heat given and received by all bodies participating in heat exchange is equal to zero.

In doing so, the following applies sign rule:

• the amount of heat received by the body is considered positive, given - negative.

*Heat capacity of gases

Literature

1. Aksenovich L. A. Physics in high school: Theory. Tasks. Tests: Proc. allowance for institutions providing general. environments, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsia i vykhavanne, 2004. - C. 129-133, 152-161.
2. Zhilko V.V. Physics: Proc. allowance for the 11th grade. general education school from Russian lang. training / V.V. Zhilko, A.V. Lavrinenko, L.G. Markovich. - Mn.: Nar. asveta, 2002. - S. 125, 128-132.

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

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

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

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

Formula of the first law of thermodynamics

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

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

Processes of the first law of thermodynamics

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

First law of thermodynamics for an isochoric process

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

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

From this comes the following formula:

Q = ΔU = U (T2) - U (T1).

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

First law of thermodynamics for isobaric process

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

A = p (V2 - V1) = p ∆V.

The isobaric first law of thermodynamics gives:

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

Application of the first law of thermodynamics

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

First law of thermodynamics video

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

It represents the law of conservation of energy, one of the universal laws of nature (along with the laws of conservation of momentum, charge and symmetry):

Energy is indestructible and uncreated; it can only change from one form to another in equivalent proportions.

The first law of thermodynamics is yourself postulate- it cannot be proven logically or deduced from any more general provisions. The truth of this postulate is confirmed by the fact that none of its consequences is in conflict with experience.

Here are some more formulations of the first law of thermodynamics:

- The total energy of an isolated system is constant;

- A perpetual motion machine of the first kind is impossible (an engine that does work without expending energy).

First law of thermodynamics establishes the relationship between the heat Q, the work A and the change in the internal energy of the system? U:

Change in internal energy system is equal to the amount of heat communicated to the system minus the amount of work done by the system against external forces.

dU = δQ-δA (1.2)

Equation (1.1) is mathematical notation of the 1st law of thermodynamics for the finite, equation (1.2) - for an infinitely small change in the state of the system.

Internal energy is a state function; this means that the change in internal energy? U does not depend on the path of the system transition from state 1 to state 2 and is equal to the difference between the values ​​of internal energy U 2 and U 1 in these states:

U \u003d U 2 -U 1 (1.3)

It should be noted, that it is impossible to determine the absolute value of the internal energy of the system; thermodynamics is only interested in the change in internal energy during a process.

Consider an application the first law of thermodynamics to determine the work done by the system in various thermodynamic processes (we will consider the simplest case - the work of expanding an ideal gas).

Isochoric process (V = const; ?V = 0).

Since the work of expansion is equal to the product of pressure and volume change, for an isochoric process we get:

Isothermal process (T = const).

From the equation of state of one mole of an ideal gas, we obtain:

δA = PdV = RT(I.7)

Integrating expression (I.6) from V 1 to V 2 , we obtain

A=RT= RTln= RTln (1.8)

Isobaric process (P = const).

Qp = ?U + P?V (1.12)

In equation (1.12) we group variables with the same indices. We get:

Q p \u003d U 2 -U 1 + P (V 2 -V 1) \u003d (U 2 + PV 2) - (U 1 + PV 1) (1.13)

Let's introduce a new system state function - enthalpy H, identically equal to the sum of internal energy and the product of pressure and volume: Н = U + PV. Then expression (1.13) is transformed to the following form:

Qp= H 2 -H 1 =?H(1.14)

Thus, the thermal effect of an isobaric process is equal to the change in the enthalpy of the system.

Adiabatic process (Q= 0, δQ= 0).

In an adiabatic process, the expansion work is done by reducing the internal energy of the gas:

A = -dU=C v dT (1.15)

If Cv does not depend on temperature (which is true for many real gases), the work done by the gas during its adiabatic expansion is directly proportional to the temperature difference:

A \u003d -C V ?T (1.16)

Task number 1. Find the change in internal energy during the evaporation of 20 g ethanol at its boiling point. The specific heat of vaporization of ethyl alcohol at this temperature is 858.95 J/g, the specific vapor volume is 607 cm 3 /g (disregard the volume of liquid).

Solution:

1 . Calculate the heat of evaporation 20 g of ethanol: Q=q beat m=858.95J/g 20g = 17179J.

2 .Calculate the work on changing the volume 20 g of alcohol during its transition from a liquid state to a vapor state: A \u003d P? V,

where R- alcohol vapor pressure, equal to atmospheric, 101325 Pa (because any liquid boils when its vapor pressure is equal to atmospheric pressure).

V \u003d V 2 -V 1 \u003d V W -V p, because V<< V п, то объмом жидкости можно пренебречь и тогда V п =V уд ·m. Cледовательно, А=Р·V уд ·m. А=-101325Па·607·10 -6 м 3 /г·20г=-1230 Дж

3. Calculate the change in internal energy:

U \u003d 17179 J - 1230 J \u003d 15949 J.

Since? U> 0, then, consequently, when ethanol evaporates, an increase in the internal energy of alcohol occurs.