WORK (in thermodynamics) WORK (in thermodynamics)

WORK, in thermodynamics:
1) one of the forms of energy exchange (along with heat) of a thermodynamic system (physical body) with surrounding bodies;
2) quantitative characteristics of energy conversion in physical processes depend on the type of process; The work of a system is positive if it gives out energy, and negative if it receives.

Encyclopedic Dictionary. 2009 .

See what “WORK (in thermodynamics)” is in other dictionaries:

work (in thermodynamics)- work Energy transferred from one body to another, not associated with the transfer of heat and (or) matter. [Collection of recommended terms. Issue 103. Thermodynamics. Academy of Sciences of the USSR. Committee of Scientific and Technical Terminology. 1984] Topics… … Technical Translator's Guide

1) one of the forms of energy exchange (along with heat) of a thermodynamic system (physical body) with surrounding bodies; 2) quantitative characteristics of energy conversion in physical processes depend on the type of process; system operation... ... Encyclopedic Dictionary

Force, a measure of the action of a force, depending on the numerical magnitude and direction of the force and on the movement of the point of its application. If the force F is constant numerically and in direction, and the displacement M0M1 is rectilinear (Fig. 1), then P. A = F s cosa, where s = M0M1, and the angle... ... Physical encyclopedia

- (in thermodynamics), 1) one of the forms of exchange of energy (along with heat) of a thermodynamic system (physical bodies) with surrounding bodies; 2) quantitative characteristics of energy conversion in physical processes; depends on the type of process.... ... Modern encyclopedia

In thermodynamics:..1) one of the forms of energy exchange (along with heat) of a thermodynamic system (physical body) with surrounding bodies;..2) a quantitative characteristic of energy conversion in physical processes, depends on the type of process;… … Big Encyclopedic Dictionary

Force, a measure of the action of a force, depending on the numerical magnitude and direction of the force and on the movement of the point of its application. If the force F is numerically and directionally constant, and the displacement M0M1 is rectilinear (Fig. 1), then P. A = F․s․cosα, where s = M0M1 … Great Soviet Encyclopedia

JOB- (1) scalar physical. a value characterizing the transformation (see) from one form to another, occurring in the physical being considered. process. Unit of work in SI (see). The R. of all internal and external forces acting on a mechanical system is equal to... ... Big Polytechnic Encyclopedia

1) a quantity characterizing the transformation of energy from one form to another, occurring in the physical entity under consideration. process. For example, R. of all external and internal forces acting on mechanical system is equal to the change in the kinetic energy of the system.... ... Big Encyclopedic Polytechnic Dictionary

In thermodynamics, 1) one of the forms of energy exchange (along with heat) is thermodynamic. systems (physical bodies) with surrounding bodies; 2) quantities. characteristic of energy conversion into physical. processes, depends on the type of process; R. of the system is positive,... ... Natural science. Encyclopedic Dictionary

Work Dimension L2MT−2 Units of measurement SI J CGS ... Wikipedia

Books

• Set of tables. Physics. Thermodynamics (6 tables), . Educational album of 6 sheets. Internal energy. Gas work in thermodynamics. The first law of thermodynamics. Second law of thermodynamics. Adiabatic process. Carnot cycle. Art. 2-090-661. 6…
• Basics of molecular dynamics modeling, Galimzyanov B.N.. In the present textbook presents the basic material necessary to acquire knowledge and primary skills in computer modeling of molecular dynamics. The benefit includes...

The internal energy of a gas changes when it transitions from one state to another. Let's consider how this change is related to the work of external forces on the gas or the gas against external forces. To do this, consider a cylinder with a movable piston. In an arbitrary small area, when the piston moves, the volume of gas changes and work is done equal to the product of the force acting on the piston from the gas located inside the cylinder and the movement of the piston under the influence of this force: Δ A i = F iΔ x.Work is positive if the direction of force and displacement coincide and negative if they are opposite. It follows from this that when a gas is compressed, the work of external forces is positive, and when it expands positive work is performed by a gas. To calculate the work done by a gas when its volume changes, in the defining equation of work, you can replace the force acting on the piston in the cylinder through the product of the gas pressure and the area of ​​the piston. We find that work in thermodynamics is determined by the product of gas pressure and the change in its volume:

Δ A i = p i SΔ x = p iΔ V.

Thermodynamic work- a method of energy transfer associated with changes in the external parameters of the system.

Mechanical work is defined as:

δA=(F→dr−→), where F→ - strength, and dr−→ - elementary (infinitesimal) displacement. The elementary work of a thermodynamic system on the external environment can be calculated as follows:

δA=(F→dr−→)=P(ds−→dr−→)=PdV, Where ds−→ - normal of an elementary (infinitesimal) area, P- pressure and dV- an infinitesimal increase in volume. The work in the thermodynamic process 1→2 is thus expressed as follows: A=∫12PdV.

The amount of work depends on the path along which the thermodynamic system transitions from state 1 to state 2, and is not a function of the state of the system. This is easy to prove if you consider that geometric meaning definite integral - the area under the graph of the curve. Since work is determined through an integral, depending on the path of the process, the area under the curve, and therefore the work, will be different. Such quantities are called functions of the process. Despite the fact that the designation work is still used in physical chemistry A, according to IUPAC recommendations, work in chemical thermodynamics should be denoted as W. However, the authors can use any notation they want, as long as they give them a decoding.

The internal energy of a thermodynamic system can change in two ways: through work done on the system and through heat exchange with environment. The energy that a body receives or loses in the process of heat exchange with the environment is called amount of heat or just warmth. Heat is one of the basic thermodynamic quantities in classical phenomenological thermodynamics. The amount of heat is included in the standard mathematical formulations of the first and second laws of thermodynamics. To change the internal energy of a system through heat exchange, work must also be done. However, this is not macroscopic work that is associated with moving the boundary of the system. At the microscopic level, this work consists of the work of forces acting on the molecules of the system at the boundary of contact of a more heated body with a less heated one, that is, energy is transferred through collisions of molecules. Therefore, from the point of view of molecular kinetic theory, the difference between work and heat manifests itself only in the fact that the performance of mechanical work requires the ordered movement of molecules on a macroscopic scale, and the transfer of energy from a more heated body to a less heated one does not require this. Energy can also be transferred by radiation from one bodies to another and without their direct contact. The amount of heat is not a function of state, and the amount of heat received by a system in any process depends on the way in which it was transferred from the initial state to the final state. The unit of measurement in International system units (SI) are joule. The calorie is also used as a unit of heat measurement. IN Russian Federation calorie is approved for use as a non-systemic unit without a time limit with the scope of application “industry”.

Definition

The amount of heat is included in the mathematical formulation of the first law of thermodynamics, which can be written as ΔQ = A + ΔU. Here ΔU- change in the internal energy of the system, ΔQ is the amount of heat transferred to the system, and A- work done by the system. However, the definition of heat must indicate the method of its measurement, regardless of the first principle. Since heat is the energy transferred during heat exchange, a test calorimetric body is needed to measure the amount of heat. By changing the internal energy of the test body, it will be possible to judge the amount of heat transferred from the system to the test body. Without the use of a test body, the first principle loses the meaning of a meaningful law and turns into a determination of the amount of heat that is useless for calculations. Let in a system consisting of two bodies X And Y, body Y(test) is enclosed in a rigid adiabatic shell. Then it is not capable of performing macroscopic work, but can exchange energy (that is, heat) with the body X. Let's assume that the body X is also almost completely enclosed in an adiabatic, but not rigid shell, so that it can perform mechanical work, but can only exchange heat with Y. The amount of heat, transferred to the body X in some process, the quantity is called Q X = −ΔU Y, Where ΔU Y- change in internal energy of the body Y. According to the law of conservation of energy, full time job performed by the system is equal to the decrease in the total internal energy of the system of two bodies: A = −ΔU x − ΔUy, Where A- macroscopic work done by the body X, which allows us to write this relationship in the form of the first law of thermodynamics: ΔQ = A +ΔU x Thus, the amount of heat introduced in phenomenological thermodynamics can be measured by means of a calorimetric body (the change in internal energy of which can be judged by the reading of the corresponding macroscopic device). From the first law of thermodynamics it follows that the introduced definition of the amount of heat is correct, that is, the independence of the corresponding quantity from the choice of test body Y and the method of heat exchange between bodies. With this determination of the amount of heat, the first law becomes a meaningful law that allows experimental verification, since all three quantities included in the expression for the first law can be measured independently.

First law of thermodynamics- one of the three basic laws of thermodynamics, is the law of conservation of energy for thermodynamic systems. The first law of thermodynamics was formulated in mid-19th century as a result of the work of the German scientist J. R. Mayer, the English physicist J. P. Joule and the German physicist G. Helmholtz. According to the first law of thermodynamics, a thermodynamic system can perform work only due to its internal energy or any external energy sources. The first law of thermodynamics is often formulated as the impossibility of the existence of a perpetual motion machine of the first kind, which would do work without drawing energy from any source.

If an infinitesimal expansion of a system due to the supply of heat to it occurs in an external environment that is everywhere under the same pressure P, then an increase in the volume of the system V by an infinitesimal value dV is accompanied by work:

which the system performs on the environment and is called volume change work (mechanical work).

When the volume of a body changes from volume value to value, the work done by the system will be equal to:

From formula (*) it follows that and always have the same signs:

If , then and , i.e. during expansion, the work of the body is positive, while the body itself does the work;

If , then and , i.e., during compression, the work of the body is negative: this means that it is not the body that does the work, but work from the outside is expended on its compression.

Now, let's consider the work that the system does on some external object. Let the body in question be a gas located in a cylinder under a piston. The piston is loaded with a load on top.

As a result of the supply of heat to the gas, it expanded from volume to volume. At the same time, the piston with the load moved from height to height.

As a result of expansion, the work done by the body is:

and the potential energy of the load increased by:

The difference between the work of expansion and the increment of potential energy represents the useful external work (disposed or technical work) that is performed by the body on the external object:

The -diagram is widely used in thermodynamics. Since the state of a thermodynamic system is determined by two parameters, it is represented by a dot on the -diagram. In the figure, point 1 corresponds to the initial state of the system, point 2 to the final state, and line 1-2 corresponds to the process of expansion of the working fluid from to .

Mechanical work is graphically depicted on a plane with an area enclosed between the process curve and the volume axis.

The work being done is graphically depicted on a plane with an area enclosed between the process curve and the pressure axis.

The work depends on the nature of the thermodynamic process.

First law of thermodynamics.

The first law of thermodynamics is the law of conservation and transformation of energy.

For thermodynamic processes, the law establishes the relationship between heat, work and changes in the internal energy of the thermodynamic system.

Statement of the first law of thermodynamics:

The heat supplied to the system is spent on changing the energy of the system and performing mechanical work.

For 1 kg of substance, the equation of the first law of thermodynamics has the form:

The first law of thermodynamics can also be written in another form.

Considering that the enthalpy is equal to:

and its change:

Let us express the change in internal energy from the expression:

and substitute it into the equation of the first law of thermodynamics

Until now, we have considered only systems in which matter did not move in space. However, it should be noted that the first law of thermodynamics is of a general nature and is valid for any thermodynamic systems, both stationary and moving.

Let us assume that the working fluid is supplied to a thermomechanical unit (for example, turbine blades). The working fluid performs technical work, for example, driving a turbine rotor, and then is removed through the exhaust pipe.

Let us write the first law of thermodynamics for a stationary system:

The work of expansion is performed by the working fluid on the surfaces that limit the selected moving volume, i.e., on the walls of the unit. Part of the walls of the unit is motionless, and the work of expansion on them is zero. The other part of the walls is specially made movable (working blades in a turbine), and the working fluid performs technical work on them.

When a worker enters the unit and exits the unit, the so-called repression work:

Part of the expansion work () is spent on increasing the kinetic energy of the working fluid in the flow, equal to .

Thus:

Substituting this expression for mechanical work into the equation of the first law of thermodynamics, we obtain:

Since the enthalpy is:

The final form of the first law of thermodynamics for a moving flow will be:

The heat supplied to the flow of the working fluid is spent to increase the enthalpy of the working fluid, production technical work and an increase in the kinetic energy of the flow.

Second law of thermodynamics.

The first law of thermodynamics states that heat can be converted into work, and work into heat. Work can be completely converted into heat, for example, by friction, but heat cannot be completely converted into work in a periodically repeating (continuous) process.

The first law of thermodynamics “allows” to create a heat engine that completely converts the supplied heat into work L, i.e.:

The second law imposes more stringent restrictions and states that the work must be less than the heat supplied () by the amount of heat removed, i.e.:

Perpetual motion machine can be accomplished if heat is transferred from a cold source to a hot one. But for this, heat must spontaneously transfer from a cold body to a hot one, which is impossible.

Heat can only transfer by itself from hotter bodies to colder ones. The transfer of heat from cold bodies to heated ones does not occur by itself. This requires additional energy.

Thus, for a complete analysis of phenomena and processes, it is necessary to have, in addition to the first law of thermodynamics, an additional law. This law is second law of thermodynamics. It establishes whether a particular process is possible or impossible, in which direction the process proceeds, when thermodynamic equilibrium is achieved, and under what conditions maximum work can be obtained. One of the formulations second law of thermodynamics:

For a heat engine to exist, 2 sources are needed - hot spring and cold spring(environment).

The energy of any system, generally speaking, depends not only on the properties of the system itself, but also on external conditions. 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 energy, transmitted (or received) by the body when performing 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. External parameter in 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 believe 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 external work can be calculated 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 It also depends 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

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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 motion 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 simply be 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 said to be 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:

F → ⋅ Δ s → = − ∇ → E p ⋅ Δ s → = − Δ E p ⇒ − Δ E p = Δ E k ⇒ Δ (E k + E p) = 0 (\displaystyle (\vec (F) )\cdot \Delta (\vec (s))=-(\vec (\nabla ))E_(p)\cdot \Delta (\vec (s))=-\Delta E_(p)\Rightarrow -\Delta E_(p)=\Delta E_(k)\Rightarrow \Delta (E_(k)+E_(p))=0) .

This result is known as the law of conservation of mechanical energy and states that the total mechanical energy in closed system, in which conservative forces operate,

∑ 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

Main article: Thermodynamic work

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.

Basic formulas of thermodynamics and molecular physics, which will be useful to you.
Another great day for hands-on physics lessons. Today we will put together the formulas that are most often used to solve problems in thermodynamics and molecular physics.

So, let's go. Let us try to present the laws and formulas of thermodynamics briefly.

Ideal gas

Ideal gas is an idealization, just like a material point. The molecules of such a gas are material points, and the collisions of molecules are absolutely elastic. We neglect the interaction of molecules at a distance. In problems in thermodynamics, real gases are often taken to be ideal. It's much easier to live this way, and you don't have to deal with a lot of new terms in the equations.

So, what happens to the molecules of an ideal gas? Yes, they are moving! And it is reasonable to ask, at what speed? Of course, in addition to the speed of molecules, we are also interested in general condition our gas. What pressure P does it exert on the walls of the vessel, what volume V does it occupy, what is its temperature T.

To find out all this, there is the ideal gas equation of state, or Clapeyron-Mendeleev equation

Here m – mass of gas, M - his molecular weight(we find it from the periodic table), R – universal gas constant equal to 8.3144598(48) J/(mol*kg).

The universal gas constant can be expressed in terms of other constants ( Boltzmann's constant and Avogadro's number )

Massat , in turn, can be calculated as the product density And volume .

Basic equation of molecular kinetic theory (MKT)

As we have already said, gas molecules move, and the higher the temperature, the faster. There is a relationship between gas pressure and the average kinetic energy E of its particles. This connection is called basic equation of molecular kinetic theory and has the form:

Here n – concentration of molecules (the ratio of their number to volume), E – average kinetic energy. They can be found, as well as the root mean square speed of molecules, accordingly, using the formulas:

Substitute energy into the first equation, and we get another form of the basic equation MKT

The first law of thermodynamics. Formulas for isoprocesses

Let us remind you that the first law of thermodynamics states: the amount of heat transferred to the gas goes to change the internal energy of the gas U and to perform work A by the gas. The formula of the first law of thermodynamics is written as follows:

As you know, something happens to gas, we can compress it, we can heat it. In this case, we are interested in processes that occur at one constant parameter. Let's look at what the first law of thermodynamics looks like in each of them.

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Isothermal process occurs at a constant temperature. The Boyle-Mariotte law applies here: in an isothermal process, the pressure of a gas is inversely proportional to its volume. In an isothermal process:

proceeds at a constant volume. This process is characterized by Charles' law: At constant volume, pressure is directly proportional to temperature. In an isochoric process, all the heat supplied to the gas goes to change its internal energy.

runs at constant pressure. Gay-Lussac's law states that at constant gas pressure, its volume is directly proportional to the temperature. In an isobaric process, heat goes both to change the internal energy and to do work by the gas.

. An adiabatic process is a process that occurs without heat exchange with the environment. This means that the formula of the first law of thermodynamics for an adiabatic process looks like this:

Internal energy of a monatomic and diatomic ideal gas

Heat capacity

Specific heat equal to the amount of heat required to heat one kilogram of a substance by one degree Celsius.

In addition to specific heat capacity, there is molar heat capacity (the amount of heat required to heat one mole of a substance by one degree) at constant volume, and molar heat capacity at constant pressure. In the formulas below, i is the number of degrees of freedom of gas molecules. For a monatomic gas i=3, for a diatomic gas – 5.

Thermal machines. Efficiency formula in thermodynamics

Heat engine , in the simplest case, consists of a heater, a refrigerator and a working fluid. The heater imparts heat to the working fluid, it does work, then it is cooled by the refrigerator, and everything repeats. O v. A typical example of a heat engine is an internal combustion engine.

Efficiency heat engine is calculated by the formula

So we have collected the basic formulas of thermodynamics that will be useful in solving problems. Of course, these are not all formulas from the topic of thermodynamics, but knowledge of them can really serve you well. And if you have any questions, remember student service, whose specialists are ready to come to the rescue at any time.