What is work equal to in thermodynamics? Work in thermodynamics

The energy of any system, generally speaking, depends not only on the properties of the system itself, but also on external conditions. The external conditions in which the system is located can be characterized by specifying certain quantities called external parameters. One of these parameters, as already noted, is the volume of the system. The interaction of bodies, during which their external parameters change, is called mechanical interaction, and the process of transferring energy from one body to another during such interaction is called work. The term “work” is also used to denote a physical quantity equal to the energy transferred (or received) by a body when doing work.

In mechanics, work is defined as the product of the projection of force on the direction of movement and the magnitude of movement. Work is done when a force acts on a moving body and is equal to the change in its kinetic energy. In thermodynamics, the motion of a body as a whole is not considered. Here, the work done by the system (or on the system) is associated with a displacement of its boundaries, i.e. with a change in its volume. This occurs, for example, during the expansion (or compression) of gas located in a cylinder under the piston. In equilibrium processes, the elementary work done by a gas (or on a gas) with an infinitesimal change in volume is determined as

Where dh– infinitesimal displacement of the piston (system boundaries), p– gas pressure. We see that when the gas expands ( ) the work he does is positive ( ), and when compressed ) – negative ( ).

The same expression determines the work done by any thermodynamic system (or on a system) with an infinitesimal change in volume. From formula (5.4) it follows that if the system itself does work (which occurs during expansion), then the work is positive, but if work is done on the system (during compression), then the work performed by it is negative. As we see, in thermodynamics the signs of work are opposite to the signs of work in mechanics.

With a final change in volume from V 1 to V 2 work can be determined by integrating elementary work ranging from V 1 to V 2:

(5.5)

The numerical value of the work is equal to the area of ​​the curvilinear trapezoid bounded by the curve and straight And (Fig. 5.1). Since the area limited by the axis V and curve p(V), is different, then the thermodynamic work will be different. It follows that thermodynamic work depends on the path of transition of the system from state 1 to state 2 and in a closed process (cycle) it is not equal to zero. The operation of all heat engines is based on this (this will be discussed in detail in paragraph 5.7).

We use this formula to obtain the work done by a gas under various isoprocesses. In an isochoric process V= const, and

Rice. 5.1

work for that A= 0. For an isobaric process p= const work . In an isothermal process, in order to integrate according to formula (5.5), one should express in its integrand function p through V according to the formula of the Clapeyron–Mendeleev law:

Where – number of moles of gas. Taking this into account, we get

(5.6)

Internal energy, according to formula (5.1), can change both due to a change (increase or decrease) in the energy levels of the system, and due to the redistribution of the probabilities of its various states, i.e. due to transitions of the system from one state to another. The performance of thermodynamic work is associated only with a displacement (or deformation) of the energy levels of the system without changing its distribution among states, i.e. without changing the probabilities. Thus, in the case of a system consisting of non-interacting particles (as, for example, in the case of an ideal gas), when we can talk about the energies of individual particles, the performance of work is associated with a change in the energy of individual particles ( ) with a constant number of particles at each energy level. This is shown schematically in Fig. 1 using the example of the simplest two-level system. 5.2. For example

Rice. 5.2

Measures, when a gas is compressed by a piston, the piston, moving, imparts the same energy to all molecules colliding with it, which transfer energy to the molecules of the next layer, etc. As a result, the energy of each particle increases by the same amount. As another simple example of the dependence of the energy levels of a system on its external parameter, we can give the expression for the energy of a microparticle in a one-dimensional infinitely deep potential well

Where m– particle mass, l– size of the particle motion region, n– an integer excluding zero. The external parameter in this case is the width of the pit. When the width of the well changes, the energy levels shift by As the pit width increases energy levels shift down , and when decreasing – up

Unlike mechanical work, which is equal to the change in the kinetic energy of a body, thermodynamic work is equal to the change in its internal energy.

It should also be noted that thermodynamic work, like mechanical work, is performed during the process of changing state, therefore it depends on the type of process and is not a function of state.

6.3. Work in thermodynamics

Earlier, in paragraph 6.1, we talked about the equilibrium states of a thermodynamic system; in these states, the parameters of the system are identical throughout its entire volume. When starting to consider work in thermodynamic systems, we should expect that its implementation is associated with a change in the volume of the system. And then the question arises, what processes are we talking about if equilibrium states are to be considered? The answer is as follows: if the process is slow, then the values ​​of the state parameters throughout the entire volume can be considered the same. The concept of “slow” needs to be clarified here. First of all, it is associated with the concept of “relaxation time” - the time during which equilibrium is established in the system. We are now interested in the time of pressure equalization in the system (relaxation time), when the thermodynamic system performs work associated with a change in volume; for a homogeneous gas this time is ~ 10–16 s. Obviously, the relaxation time is quite small compared to the time of processes in real thermodynamic systems (or compared to the measurement time). Naturally, we have the right to assume that the real process is a sequence of equilibrium states and therefore we have the right to depict it as a line on the graph V, P(Fig. 6.1.). Of course, volume and temperature or pressure and temperature can be plotted along the axes of the coordinate system. Since in algebra, and not only, when plotting graphs, the first coordinate axis is read and written X, and then - at, i.e. " X, at", it is hoped that the reader, reading the "axes of the coordinate system V, R", assumes - along the axis X volume is deposited V, and along the axis at– gas pressure R.

Let's get acquainted with the type of lines that graphically display the simplest processes in a coordinate system, along the axes of which state parameters are plotted V, P(other coordinate axes are possible). The choice of the coordinate system is due to the fact that the area limited by the process curve and the two extreme coordinates for the initial and final volume values ​​is equal to the work of compression or expansion. In Fig. Figure 6.2 shows graphs of isoprocesses drawn from the same initial state. The curve of an adiabatic process (adiabatic) is steeper than for an isothermal process (isotherm). This circumstance can be explained on the basis of the Clapeyron equation for the state of gases:

(2)

Expressing from the equation of state R 1 and R 2, pressure difference during gas expansion from volume V 1 to volume V 2 will be written:

. (3)

Here, as in equation (2),
.

During adiabatic expansion, work on external bodies is performed only due to the internal energy of the gas, as a result of which the internal energy, and with it the temperature of the gas, decreases; i.e. at the end of the adiabatic expansion process (Fig. 6.2) T 2 < T 1 (find a rationale); in an isothermal process T 2 T 1. Therefore, in formula (3) the pressure difference
with adiabatic expansion it will be greater than with isothermal expansion (check by carrying out transformations).

Realizing that we are dealing with equilibrium processes and familiarizing ourselves with their graphical display in the coordinate system ( V,P), let's move on to searching for an analytical expression for the external work performed by a thermodynamic system.

The work performed by the system can be calculated depending on the value of external forces acting on the system, and on the amount of deformation of the system - changes in its shape and size. If external forces are applied along the surface in the form, for example, of external pressure compressing the system, then the calculation of the external work can be made depending on the change in the volume of the system. To illustrate, consider the process of expansion of a gas enclosed in a cylinder with a piston (Fig. 6.3). Let us assume that the external pressure in all areas along the surface of the cylinder is the same. If, during the expansion of the system, the piston moves a distance dl, then the elementary work performed by the system will be written: dA F ds p S dl p dV; Here S is the area of ​​the piston, and S dl dV– change in the volume of the system (Fig. 6.3). When the system expands, the external pressure does not always remain constant, so the work done
system when its volume changes from V 1 to V 2 should be calculated as the sum of elementary works, i.e. by integration:
. From the work equation it follows that the parameters of the initial ( p 1 ,V 1) and final ( p 2 ,V 2) the states of the system do not determine the amount of external work performed; you also need to know the function r(V), revealing the change in pressure during the transition of a system from one state to another.

In conclusion, it should be noted heat exchange between the system and the environment depends not only on the parameters of the initial and final states of the system, but also on the sequence of intermediate states through which the system passes. This follows from the first law of thermodynamics: Q U 2 –U 1 A, Where U 1 and U 2 are determined only by setting the parameters of the initial and final states, and external work A depends, in addition, also on the transition process itself. As a result, the heat Q, received or given by the system during the transition from one state to another, cannot be expressed depending only on the temperature of its initial and final states.

Concluding the excursion to the section “Thermodynamics. The first law of thermodynamics,” we list its key concepts: thermodynamic system, thermodynamic parameters, equilibrium state, equilibrium process, reversible process, internal energy of the system, first law of thermodynamics, work of a thermodynamic system, adiabatic process.

Mechanical work

Mechanical work- this is a physical quantity - a scalar quantitative measure of the action of a force (resultant forces) on a body or forces on a system of bodies. Depends on the numerical magnitude and direction of the force(s), and on the movement of the body (system of bodies).

Notations used

The job is usually designated by the letter A(from German. A rbeit- work, labor) or letter W(from English w ork- work, labor).

Definition

Work of force applied to a material point

The total work of moving one material point, performed by several forces applied to this point, is defined as the work of the resultant of these forces (their vector sum). Therefore, further we will talk about one force applied to a material point.

With rectilinear motion of a material point and a constant value of the force applied to it, the work (of this force) is equal to the product of the projection of the force vector onto the direction of movement and the length of the displacement vector made by the point:

A = F s s = F s c o s (F , s) = F → ⋅ s → (\displaystyle A=F_(s)s=Fs\ \mathrm (cos) (F,s)=(\vec (F))\ cdot(\vec(s)))

Here the dot denotes the scalar product, s → (\displaystyle (\vec (s))) is the displacement vector; it is assumed that the acting force F → (\displaystyle (\vec (F))) is constant during the time for which the work is calculated.

In the general case, when the force is not constant and the movement is not rectilinear, the work is calculated as a curvilinear integral of the second kind along the trajectory of the point:

A = ∫ F → ⋅ d s → . (\displaystyle A=\int (\vec (F))\cdot (\vec (ds)).)

(this implies summation along a curve, which is the limit of a broken line composed of successive movements d s → , (\displaystyle (\vec (ds)),) if we first consider them finite, and then direct the length of each to zero).

If there is a dependence of the force on the coordinates, the integral is defined as follows:

A = ∫ r → 0 r → 1 F → (r →) ⋅ d r → (\displaystyle A=\int \limits _((\vec (r))_(0))^((\vec (r)) _(1))(\vec (F))\left((\vec (r))\right)\cdot (\vec (dr))) ,

where r → 0 (\displaystyle (\vec (r))_(0)) and r → 1 (\displaystyle (\vec (r))_(1)) are the radius vectors of the initial and final position of the body, respectively.

• Consequence. If the direction of the applied force is orthogonal to the displacement of the body, or the displacement is zero, then the work (of this force) is zero.

Work of forces applied to a system of material points

The work of forces to move a system of material points is defined as the sum of the work of these forces to move each point (the work done on each point of the system is summed up into the work of these forces on the system).

Even if the body is not a system of discrete points, it can be divided (mentally) into many infinitesimal elements (pieces), each of which can be considered a material point and the work can be calculated in accordance with the definition above. In this case, the discrete sum is replaced by an integral.

• These definitions can be used both to calculate the work done by a particular force or class of forces, and to calculate the total work done by all forces acting on a system.

Kinetic energy

Kinetic energy is introduced in mechanics in direct connection with the concept of work.

The scheme of reasoning is as follows: 1) let's try to write down the work done by all forces acting on a material point and, using Newton's second law (which allows us to express force through acceleration), try to express the answer only through kinematic quantities, 2) making sure that this was successful, and that this answer depends only on the initial and final state of motion, let's introduce a new physical quantity through which this work will be simply expressed (this will be kinetic energy).

If A t o t a l (\displaystyle A_(total)) is the total work done on the particle, defined as the sum of the work done by the forces applied to the particle, then it is expressed as:

A t o t a l = Δ (m v 2 2) = Δ E k , (\displaystyle A_(total)=\Delta \left((\frac (mv^(2))(2))\right)=\Delta E_(k ),)

where E k (\displaystyle E_(k)) is called kinetic energy. For a material point, kinetic energy is defined as half the product of the mass of this point by the square of its speed and is expressed as:

E k = 1 2 m v 2 . (\displaystyle E_(k)=(\frac (1)(2))mv^(2).)

For complex objects consisting of many particles, the kinetic energy of the body is equal to the sum of the kinetic energies of the particles.

Potential energy

A force is called potential if there is a scalar function of coordinates, known as potential energy and denoted E p (\displaystyle E_(p)), such that

F → = − ∇ E p . (\displaystyle (\vec (F))=-\nabla E_(p).)

If all forces acting on a particle are conservative, and E p (\displaystyle E_(p)) is the total potential energy obtained by summing the potential energies corresponding to each force, then:

This result is known as the law of conservation of mechanical energy and states that the total mechanical energy in a closed system subject to conservative forces is

∑ E = E k + E p (\displaystyle \sum E=E_(k)+E_(p))

is constant in time. This law is widely used in solving problems of classical mechanics.

Work in thermodynamics

In thermodynamics, the work done by a gas during expansion is calculated as the integral of pressure over volume:

A 1 → 2 = ∫ V 1 V 2 P d V . (\displaystyle A_(1\rightarrow 2)=\int \limits _(V_(1))^(V_(2))PdV.)

The work done on the gas coincides with this expression in absolute value, but is opposite in sign.

• A natural generalization of this formula is applicable not only to processes where pressure is a single-valued function of volume, but also to any process (represented by any curve in the plane PV), in particular, to cyclic processes.
• In principle, the formula is applicable not only to gas, but also to anything capable of exerting pressure (it is only necessary that the pressure in the vessel be the same everywhere, which is implicit in the formula).

This formula is directly related to mechanical work. Indeed, let's try to write the mechanical work during the expansion of the vessel, taking into account that the gas pressure force will be directed perpendicular to each elementary area, equal to the product of pressure P per area dS platforms, and then the work done by the gas to displace h one such elementary site will be

D A = P d S h . (\displaystyle dA=PdSh.)

It can be seen that this is the product of pressure and volume increment near a given elementary area. And summing up over all dS we get the final result, where there will be a complete increase in volume, as in the main formula of the paragraph.

Work of force in theoretical mechanics

Let us consider in somewhat more detail than was done above the construction of the definition of energy as a Riemannian integral.

Let a material point M (\displaystyle M) move along a continuously differentiable curve G = ( r = r (s) ) (\displaystyle G=\(r=r(s)\)) , where s is a variable arc length, 0 ≤ s ≤ S (\displaystyle 0\leq s\leq S) and it is acted upon by a force F (s) (\displaystyle F(s)) directed tangentially to the trajectory in the direction of movement (if the force is not directed tangentially, then we will understand by F (s) (\displaystyle F(s)) the projection of force on the positive tangent of the curve, thus reducing this case to the one considered below). Value F (ξ i) △ s i , △ s i = s i − s i − 1 , i = 1 , 2 , . . . , i τ (\displaystyle F(\xi _(i))\triangle s_(i),\triangle s_(i)=s_(i)-s_(i-1),i=1,2,... ,i_(\tau )) is called basic work force F (\displaystyle F) on the section G i (\displaystyle G_(i)) and is taken as an approximate value of the work produced by the force F (\displaystyle F) acting on a material point when the latter passes the curve G i (\displaystyle G_(i)) . The sum of all elementary works ∑ i = 1 i τ F (ξ i) △ s i (\displaystyle \sum _(i=1)^(i_(\tau ))F(\xi _(i))\triangle s_(i )) is the Riemann integral sum of the function F (s) (\displaystyle F(s)) .

In accordance with the definition of the Riemann integral, we can define work:

The limit to which the sum tends ∑ i = 1 i τ F (ξ i) △ s i (\displaystyle \sum _(i=1)^(i_(\tau ))F(\xi _(i))\triangle s_ (i)) all elementary work, when fineness | τ | \tau of the partition τ (\displaystyle \tau ) tends to zero is called the work of force F (\displaystyle F) along the curve G (\displaystyle G) .

Thus, if we denote this work by the letter W (\displaystyle W), then, by virtue of this definition,

W = lim | τ | → 0 ∑ i = 1 i τ F (ξ i) △ s i (\displaystyle W=\lim _\sum _(i=1)^(i_(\tau ))F(\xi _(i))\triangle s_(i)) ,

hence,

W = ∫ 0 s F (s) d s (\displaystyle W=\int \limits _(0)^(s)F(s)ds) (1).

If the position of a point on the trajectory of its movement is described using some other parameter t (\displaystyle t) (for example, time) and if the distance traveled s = s (t) (\displaystyle s=s(t)) , a ≤ t ≤ b (\displaystyle a\leq t\leq b) is a continuously differentiable function, then from formula (1) we obtain

W = ∫ a b F [ s (t) ] s ′ (t) d t . (\displaystyle W=\int \limits _(a)^(b)Fs"(t)dt.)

Dimension and units

The unit of work in the International System of Units (SI) is the joule, in the GHS it is the erg.

1 J = 1 kg m²/s² = 1 Nm 1 erg = 1 g cm²/s² = 1 dyne cm 1 erg = 10−7 J

Please give me definition-Work in thermodynamics and Adiabatic process.

Svetlana

In thermodynamics, the movement of a body as a whole is not considered and we are talking about the movement of parts of a macroscopic body relative to each other. When work is done, the volume of the body changes, but its speed remains zero. But the speeds of the molecules of the body change! Therefore, body temperature changes. The reason is that when colliding with a moving piston (gas compression), the kinetic energy of the molecules changes - the piston gives up part of its mechanical energy. When colliding with a retreating piston (expansion), the velocities of the molecules decrease and the gas cools. When work is done in thermodynamics, the state of macroscopic bodies changes: their volume and temperature.
An adiabatic process is a thermodynamic process in a macroscopic system in which the system neither receives nor releases thermal energy. The line depicting an adiabatic process on any thermodynamic diagram is called an adiabatic.

Oleg Goltsov

work A=p(v1-v2)
Where
p - pressure created by the piston = f/s
where f is the force acting on the piston
s - piston area
note p=const
v1 and v2 - initial and final volumes.

In mechanics, work A is associated with movement x body as a whole under the influence of force F

Thermodynamics deals with the movement of body parts. For example, if the gas in the cylinder under the piston expands, then by moving the piston it does work on it. In this case, the volume of gas changes (Fig. 2.1).

Let's calculate the work done by a gas when its volume changes. Elementary work when moving the piston by an amount dx equal to

.

Force is related to pressure by the relationship

Where S- piston area.

The change in volume is

Thus

(2.5)

Full work A performed by a gas when its volume changes from V 1 to V 2, we find by integrating formula (2.5)

(2.6)

Expression (2.6) is valid for any processes

Let's calculate the work during isoprocesses:

1) for an isochoric process V 1 = V 2 = const, A = 0;
2) for an isobaric process p = const, A= p( V 2 – V 1) = pΔ V;
3) for an isothermal process T= const. From equation (1.6) it follows that

.

Expression (2.6) will look like

. (2.7)

2.3. Amount of heat

The process of transferring energy from one body to another without doing work is called heat transfer.

Amount of heat- this is the energy transferred to the body as a result of heat exchange. To change the temperature of a substance by mass m from T 1 to T 2 he needs to report the amount of heat

The coefficient c in this formula is called specific heat capacity: [c]=1 J/(kg∙K).

When heating a body Q > 0, when cooling Q< 0.

2.4. The first law of thermodynamics. Application for isoprocesses.

If the system exchanges heat with surrounding bodies and does work (positive or negative), then the state of the system changes, i.e. its macroscopic parameters change. Since the internal energy U is uniquely determined by macroscopic parameters, it follows that the processes of heat exchange and work are accompanied by a change in the internal energy of the system.

The first law of thermodynamics is a generalization of the law of conservation and transformation of energy for a thermodynamic system. It is formulated as follows:

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 bodies.

The science that studies thermal phenomena is thermodynamics. Physics considers it as one of its sections, which allows one to draw certain conclusions based on the representation of matter in the form of a molecular system.

Thermodynamics, the definitions of which are built on the foundation of facts obtained experimentally, does not use accumulated knowledge about the internal. However, in some cases, this science uses molecular kinetic models to clearly illustrate its conclusions.

The support of thermodynamics is the general laws of processes occurring during changes, as well as the properties of a macroscopic system, which is considered in a state of balance. The most significant phenomenon occurring in a complex of substances is the equalization of the temperature characteristics of all its parts.

The most important thermodynamic concept is that any body possesses. It is contained in the element itself. The molecular-kinetic interpretation of internal energy is a quantity that represents the sum of the kinetic activity of molecules and atoms, as well as the potential of their interaction with each other. This implies the law discovered by Joule. It was confirmed by multiple experiments. They substantiated the fact that, in particular, it has internal energy, consisting of the kinetic activity of all its particles, which are in chaotic and disorderly movement under the influence of heat.

Working in thermodynamics changes the activity of the body. The influence of forces influencing the internal energy of a system can have both positive and negative meanings. In cases where, for example, a gaseous substance is subjected to a compression process, which is carried out in a cylindrical container under the pressure of a piston, the forces acting on it perform a certain amount of work, characterized by a positive value. At the same time, opposite phenomena occur. The gas performs negative work of the same magnitude on the piston acting on it. The actions performed by a substance are directly dependent on the area of ​​the available piston, its movement, and body pressure. In thermodynamics, the work done by a gas is positive when it expands, and negative when compressed. The magnitude of this action is directly dependent on the path along which the transition of the substance from the initial position to the final position was completed.

Work in thermodynamics of solids and liquids differs in that they change volume very slightly. Because of this, the influence of forces is often neglected. However, the result of work done on a substance may be a change in its internal activity. For example, when drilling metal parts, their temperature increases. This fact is evidence of the growth of internal energy. Moreover, this process is irreversible, since it cannot be carried out in the opposite direction.
Work in thermodynamics is one of its main ones. Its measurement is carried out in Joules. The value of this indicator is directly dependent on the path along which the system moves from the initial state to the final state. This action is not a function of the state of the body. It is a function of the process itself.

Work in thermodynamics, which is determined using available formulas, is the difference between the amount of heat supplied and removed during the closed cycle period. The value of this indicator depends on the type of process. If the system gives away its energy, this means that a positive action is being performed, and if it receives, it means a negative action.

When considering thermodynamic processes, the mechanical movement of macrobodies as a whole is not considered. The concept of work here is associated with a change in body volume, i.e. movement of parts of a macrobody relative to each other. This process leads to a change in the distance between particles, and also often to a change in the speed of their movement, therefore, to a change in the internal energy of the body.

Let there be a gas in a cylinder with a movable piston at a temperature T 1 (Fig. 1). We will slowly heat the gas to a temperature T 2. The gas will expand isobarically and the piston will move from position 1 to position 2 to a distance Δ l. The gas pressure force will do work on the external bodies. Because p= const, then the pressure force F = pS also constant. Therefore, the work of this force can be calculated using the formula

\(~A = F \Delta l = pS \Delta l = p \Delta V, \qquad (1)\)

where Δ V- change in gas volume. If the volume of the gas does not change (isochoric process), then the work done by the gas is zero.

The force of gas pressure performs work only in the process of changing the volume of gas.

When expanding (Δ V> 0) of the gas, positive work is done ( A> 0); during compression (Δ V < 0) газа совершается отрицательная работа (A < 0), положительную работу совершают внешние силы A' = -A > 0.

Let us write the Clapeyron-Mendeleev equation for two gas states:

\(~pV_1 = \frac mM RT_1 ; pV_2 = \frac mM RT_2 \Rightarrow\) \(~p(V_2 - V_1) = \frac mM R(T_2 - T_1) .\)

Therefore, in an isobaric process

\(~A = \frac mM R \Delta T .\)

If m = M(1 mol of ideal gas), then at Δ Τ = 1 K we get R = A. This implies the physical meaning of the universal gas constant: it is numerically equal to the work done by 1 mole of an ideal gas when it is heated isobarically by 1 K.

On the chart p = f(V) in an isobaric process, the work is equal to the area of ​​the shaded rectangle in Figure 2, a.

If the process is not isobaric (Fig. 2, b), then the curve p = f(V) can be represented as a broken line consisting of a large number of isochores and isobars. Work on isochoric sections is zero, and the total work on all isobaric sections will be

\(~A = \lim_(\Delta V \to 0) \sum^n_(i=1) p_i \Delta V_i\), or \(~A = \int p(V) dV,\)

those. will be equal to the area of ​​the shaded figure. In an isothermal process ( T= const) the work is equal to the area of ​​the shaded figure shown in Figure 2, c.

It is possible to determine work using the last formula only if it is known how the gas pressure changes when its volume changes, i.e. the form of the function is known p(V).

Thus, the gas does work when expanding. Devices and units whose actions are based on the property of a gas to do work during the expansion process are called pneumatic. Pneumatic hammers, mechanisms for closing and opening doors on vehicles, etc. operate on this principle.

Literature

Aksenovich L. A. Physics in secondary school: Theory. Assignments. Tests: Textbook. allowance for institutions providing general education. environment, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsiya i vyakhavanne, 2004. - P. 155-156.

« Physics - 10th grade"

As a result of what processes can internal energy change?
How is work defined in mechanics?

Work in mechanics and thermodynamics.

IN mechanics work is defined as the product of the force modulus, the displacement modulus of the point of its application and the cosine of the angle between the force and displacement vectors. When a force acts on a moving body, the work done by this force is equal to the change in its kinetic energy.

Work in thermodynamics is defined in the same way as in mechanics, but it is not equal to the change in the kinetic energy of the body, but to the change in its internal energy.

Change in internal energy when doing work.

Why does its internal energy change when a body contracts or expands? Why, in particular, does the air heat up when inflating a bicycle tire?

The reason for the change in gas temperature during its compression is as follows: during elastic collisions of gas molecules with a moving piston, their kinetic energy changes.

When compression or expansion occurs, the average potential energy of interaction between molecules also changes, since this changes the average distance between the molecules.

So, when moving towards gas molecules, the piston transfers part of its mechanical energy to them during collisions, as a result of which the internal energy of the gas increases and it heats up. The piston acts like a football player meeting the ball flying at him with a kick. The player's foot imparts a speed to the ball that is significantly greater than what it had before the impact.

Conversely, if the gas expands, then after colliding with the retreating piston, the velocities of the molecules decrease, as a result of which the gas cools. A football player acts in the same way, in order to reduce the speed of a flying ball or stop it - the football player’s leg moves away from the ball, as if giving way to it.

Let us calculate the work of the force acting on the gas from the external body (piston), depending on the change in volume, using the example of gas in a cylinder under the piston (Fig. 13.1), while the gas pressure is maintained constant. First, let's calculate the work done by the gas pressure force acting on the piston with the force ". If the piston rises slowly and evenly, then, according to Newton's third law, = ". In this case, the gas expands isobarically.

The modulus of the force acting from the gas on the piston is equal to F" = pS, where p is the gas pressure, and S is the surface area of ​​the piston. When the piston rises a short distance Δh = h 2 - h 1, the work of the gas is equal to:

A" = F"Δh = pS(h 2 - h 1) = p(Sh 2 - Sh 1). (13.2)

The initial volume occupied by the gas is V 1 = Sh 1, and the final volume V 2 = Sh 2. Therefore, we can express the work of a gas through the change in volume ΔV = (V 2 - V 1):

A" = p(V 2 - V 1) = pΔV > 0. (13.3)

When expanding, the gas does positive work, since the direction of the force and the direction of movement of the piston coincide.

If the gas is compressed, then formula (13.3) for the gas work remains valid. But now V 2< V 1 , и поэтому А < 0.

The work A performed by external bodies on the gas differs from the work A" of the gas itself only in sign:

A = -A" = -pΔV. (13.4)

When gas is compressed, when ΔV = V 2 - V 1< 0, работа внешней силы оказывается положительной. Так и должно быть: при сжатии газа направления силы и перемещения точки её приложения совпадают.

If the pressure is not maintained constant, then during expansion the gas loses energy and transfers it to surrounding bodies: a rising piston, air, etc. The gas cools down. When a gas is compressed, on the contrary, external bodies transfer energy to it and the gas heats up.

Geometric interpretation of the work. The work A" of a gas for the case of constant pressure can be given a simple geometric interpretation.

At constant pressure, the graph of the dependence of gas pressure on the volume it occupies is a straight line, parallel to the abscissa axis (Fig. 13.2). It is obvious that the area of ​​the rectangle abdc, limited by the graph рх = const, the V axis and the segments ab and cd equal to the gas pressure, is numerically equal to the work determined by formula (13.3):

A" = p1(V2 - V2) = |ab| |ac|.

In general, the gas pressure does not remain unchanged. For example, during an isothermal process it decreases in inverse proportion to the volume (Fig. 13.3). In this case, to calculate the work, you need to divide the total change in volume into small parts and calculate the elementary (small) work, and then add them all up. The work of the gas is still numerically equal to the area of ​​the figure limited by the graph of p versus V, the V axis and the segments ab and cd, the length of which is numerically equal to the pressures p 1 p 2 in the initial and final states of the gas.