NThe study of thermal phenomena is calledthermodynamics. Thermodynamics is based on the most general laws of thermal processes and properties of macroscopic systems.
When learning the basics of thermodynamics, keep the following definitions in mind. A physical system consisting of a large number of particles - atoms or molecules, which undergo thermal motion and, interacting with each other, exchange energies, is called thermodynamic system.
The state of a thermodynamic system is determined macroscopic parameters, for example specific volume, pressure, temperature.
Thermodynamics considers isolated systems of bodies in a state of thermodynamic equilibrium. This means that in such systems all observable macroscopic processes have ceased. An important property of a thermodynamically equilibrium system is the equalization of the temperature of all its parts.
Thermodynamics considers only equilibrium states, those. states in which the parameters of a thermodynamic system do not change over time.
If a thermodynamic system has been subjected to external influences, it will eventually move to another equilibrium state. This transition is called a thermodynamic process .
Thermodynamic process is called the transition of a system from the initial state to the final state through a sequence of intermediate states.
Processes can be reversible and irreversible.
Reversibleis a process in which a reverse transition of a system from the final state to the initial state through the same intermediate states is possible, so that no changes occur in the surrounding bodies. A reversible process is a physical abstraction. An example of a process approaching reversibility is the oscillation of a heavy pendulum on a long suspension. In this case, kinetic energy is almost completely converted into potential energy, and vice versa. Oscillations occur for a long time without a noticeable decrease in amplitude due to the low resistance of the medium and friction forces.
Any process accompanied by friction or heat transfer from a heated body to a cold one is irreversible. An example of an irreversible process is the expansion of a gas, even an ideal one, into vacuum. When expanding, the gas does not overcome the resistance of the medium and does not do work, but in order to reassemble all the molecules of the gas into the previous volume, i.e., bring the gas to its initial state, it is necessary to expend work. Thus, all real processes are irreversible.
Changes in the internal energy of a gas during heat exchange and work performed.
One of the most important concepts of thermodynamics is internal energy bodies. All macroscopic bodies have energy contained within the bodies themselves. From the point of view of molecular kinetic theory, the internal energy of a substance consists of the kinetic energy of all atoms and molecules and the potential energy of their interaction with each other .
Internal energy – this is the sum of the energies of molecular interactions and the energy of thermal motion of molecules.
In particular, the internal energy of an ideal gas is equal to the sum of the kinetic energies of all gas particles in continuous and random thermal motion. The internal energy of an ideal gas depends only on its temperature and does not depend on volume(Joule's law).
Molecular kinetic theory leads to the following expression for internal energy of one mole of an ideal monatomic gas(helium, neon, etc.), the molecules of which perform only translational motion:
Since the potential energy of interaction of molecules depends on the distance between them, in general the internal energy
U body depends along with temperature T also on volume V: U = U(T, V).
Thus, the internal energy of the system depends only on its state and is a unique function of the state, internal energy U body is uniquely determined by macroscopic parameters characterizing the state of the body. It does not depend on how this state was realized.
The internal energy of the body can be changed in different ways:
- Performing mechanical work.
- Heat exchange.
The internal energy of a body can change if external forces acting on it do work (positive or negative).
For example, a gas is compressed in a cylinder under a piston of area S. The piston, compressing the gas, moves with a certain speed v. Gas molecules, moving randomly, hit the piston. After the elastic impact of the molecule on the piston, the speed of the molecule increases, which means its kinetic energy also increases, which leads to an increase in the internal energy of the gas.
When a gas is compressed, its internal energy increases due to mechanical work performed by the piston. As the gas expands, its internal energy decreases, turning into mechanical energy of the piston.
When a gas is compressed, external forces perform some positive work on the gas A".
At the same time, the pressure forces acting on the piston from the gas do work
A= –A".
If the gas volume has changed by a small amount Δ V, then the gas does work pSΔx = pΔV, Where p– gas pressure, S– piston area, Δ x- its movement.
When expanding, the work done by the gas is positive, when compressing it is negative..
In the general case, when transitioning from some initial state (1) to the final state (2) gas work expressed by the formula:
or in the limit at Δ V i → 0:
Work is numerically equal to the area under the process graph on the diagram ( p, V):
The amount of work depends on how the transition from the initial state to the final state was made. In Fig. Figure 2 shows three different processes that transfer gas from state (1) to state (2). In all three cases, the gas does different work.
Figure 2.
Three different paths of transition from state (1) to state (2).
In all three cases, the gas makes various jobs, equal to the area under the process graph.
The processes shown in Fig. 2, can be carried out in the opposite direction; then work A just change the sign to the opposite one .
Processes that can be carried out in both directions are calledreversible.
Unlike gases, liquids and solids change their volume little, so that in many cases the work done during expansion or compression can be neglected. However, the internal energy of liquid and solid bodies can also change as a result of work. When parts are machined (for example, when drilling), they heat up. This means that their internal energy changes.
The internal energy of a body can change not only as a result of the work performed, but also due toheat exchange.
When bodies come into thermal contact, the internal energy of one of them can increase, while the internal energy of the other can decrease. In this case, we talk about heat flow from one body to another. The transfer of energy from one body to another in the form of heat can only occur if there is a temperature difference between them.
Let us bring two bodies with different temperatures into contact. Let the temperature of the first body be higher than that of the second. As a result of the exchange of energies, the temperature of the first body decreases, and the temperature of the second increases. In the example under consideration, the kinetic energy of the chaotic movement of the molecules of the first body transforms into kinetic energy chaotic movement of molecules of the second body.
Heat flow is always directed from a hot body to a cold one.
The process of transferring internal energy without performing mechanical work is called heat exchange.
The measure of energy received or given off by a body in the process of heat exchange is a physical quantity called amount of heat.
The amount of heatQ, received by the body is called the change in the internal energy of the body as a result of heat exchange.
Quantity of heat Q is an energy quantity. In SI, the amount of heat is measured in units of mechanical work - joules(J).
Before the introduction of SI, the amount of heat was expressed in calories.
Calorie - this is the amount of heat required to heat 1 g of distilled water by 1°C, from 19.5°C to 20.5°C.
A unit 1000 times larger than a calorie is called a kilocalorie (1 kcal = 1000 cal). The ratio between units: 1 cal = 4.19 J.
If, as a result of heat exchange, a certain amount of heat is transferred to the body, then the internal energy of the body and its temperature change.
To heat a body with massmon temperaturet 1 up to temperaturet 2 he needs to be told the amount of heat
Q = cm(t 2 – t 1 )
The amount of heat Q required to heat 1 kg of a substance by 1 K is called specific heat capacity of a substancec.
c= Q / (mΔT).
In many cases it is convenient to use molar heat capacity C:
C= M c, Where M– molar mass of the substance.
When heat is transferred from one body to another, it is always true heat balance equation, according to which the amount of heatQ 1 given by the first body is equal to the amount of heatQ 2 , received by the second body.
Q 1 = Q 2
Heat and work are not a type of energy, but a form of its transfer; they exist only in the process of energy transfer.
In real conditions, both methods of transferring energy to a system in the form of work and the form of heat usually accompany each other.
The first law of thermodynamics.
The picture shows energy flows between the thermodynamic system and surrounding bodies. as a result of heat exchange and work performed:
Magnitude Q> 0 if the heat flow is directed towards the thermodynamic system. Magnitude A> 0 if the system does positive work on surrounding bodies.
If the system exchanges heat with surrounding bodies and does work (positive or negative), then the state of the system changes, that is, its macroscopic parameters (temperature, pressure, volume) change.
The processes of heat exchange and work are accompanied by a change in Δ U internal energy of the system.
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:
Change Δ U internal energy of a non-isolated thermodynamic system is equal to the difference between the amount of heat Q, transferred to the system, and the work A, a perfect system over external bodies.
ΔU = Q – A.
The relationship expressing the first law of thermodynamics is often written in a different form:
Q= ΔU + A.
The amount of heat received by the system goes to change its internal energy and perform work on external bodies.
The first law of thermodynamics is a generalization of experimental facts. According to this law, energy cannot be created or destroyed; it is transmitted from one system to another and transformed from one form to another. If friction forces act between the bodies that make up a closed system, then part of the mechanical energy is converted into the internal energy of the bodies (heating).
During any physical interactions, energy neither appears nor disappears. It just changes from one form to another. This experimentally established fact expresses a fundamental law of nature -
No. 8, page 163
Determine Q - the heat required to melt lead with a mass of m = 10 kg, located at the melting temperature. Specific heat of fusion of lead λ=25 kJ/kg. (answer Q=250 kJ)
Fundamentals of Thermodynamics
Thermodynamics studies processes and phenomena occurring in nature and technology from the point of view of energy conversion, including the internal energy of bodies.
Thermodynamic system is a collection of bodies capable of exchanging energy with each other and with other systems. A closed thermodynamic system does not exchange energy with other systems.
Each body has a very specific structure; it consists of particles that move chaotically and interact with each other, therefore any body has internal energy.
Internal energy is a quantity that characterizes the body’s own state, i.e. the energy of the chaotic (thermal) movement of microparticles of the system (molecules, atoms, electrons, nuclei, etc.) and the energy of interaction of these particles.
The internal energy of an ideal gas consists only of the energy of molecular motion, since the interaction of molecules can be neglected. Internal energy of a monatomic ideal gas determined by the formula U = 3/2 m/M RT. Internal energy of one mole of a monatomic ideal gas:
Internal energy can be changed in two ways: by heat transfer and by performing mechanical work
Heat transfer- this is a change in internal energy without doing work: energy is transferred from more heated bodies to less heated ones. Heat transfer is of three types: thermal conductivity (direct exchange of energy between chaotically moving particles of interacting bodies or parts of the same body); convection (transfer of energy by flows of liquid or gas) and radiation (transfer of energy by electromagnetic waves). The measure of transferred energy during heat transfer is the quantity of heat (Q). It is generally accepted that Q > 0, if the body receives energy, and Q< 0
if the body gives up its energy
When committing mechanical work There must be a directed movement of bodies under the influence of forces, for example, the movement of a piston in a cylinder with gas. If the gas expands, then the force of gas pressure on the piston does positive work ( A > 0) due to the internal energy of the gas. If the external forces are greater than the gas pressure force, then the gas is compressed and the work done by the gas will be negative ( A< 0 ), while the internal energy increases.
With isobaric heating the gas does work on external forces, where V1 and V2 are the initial and final volumes of the gas. If the process is not isobaric, the amount of work can be determined by the area of the ABCD figure enclosed between the line expressing the dependence p(V) and the initial and final volumes of gas V
First law of thermodynamics :
the change in the internal energy of a closed system is equal to the sum of the amount of heat transferred to the system and the work of external forces performed on the system.
, where is the change in internal energy, Q is the amount of heat transferred to the system, A is the work of external forces. A* is the work of the system itself, i.e. the work of gas. If the system itself does work and receives or gives off heat, then the change in its internal energy.
∆U = Q – A
Application of the first law of thermodynamics to isoprocesses The temperature is constant, therefore the internal energy does not change. Then the equation of the first law of thermodynamics will take the form: , i.e., the amount of heat transferred to the system goes to perform work during isothermal expansion, which is why the temperature does not change.
In an isobaric process the gas expands and the amount of heat transferred to the gas goes to increase its internal energy and to do work: .
In an isochoric process the gas does not change its volume, therefore, no work is done by it, i.e. A = 0, and the equation of the first law has the form , i.e., the transferred amount of heat goes to increase the internal energy of the gas.
A process is called adiabatic, occurring without heat exchange with the environment. Q = 0, therefore, when the gas expands, it does work by reducing its internal energy, therefore, the gas cools,
Second law of thermodynamics states that spontaneous transfer of heat from a less heated body to a more heated body is impossible.
Equilibrium and nonequilibrium states of gas
The state of the gas system can be equilibrium or nonequilibrium. An equilibrium state is considered to be in which the gas parameters ( p, V, T) remain unchanged indefinitely, as long as any external influences will not bring the system out of this state (assumes absence of mass flows, heat, etc.).
An example of an equilibrium state is a system of water and steam placed in a closed thermally insulated vessel.
An equilibrium system is also a gas located in a thermally insulated cylinder under a piston, which is acted upon by a constant force. But a gas located in a cylinder with a movable piston can move at a certain speed from one state to another, for example, expand or contract.
During expansion, the gas immediately adjacent to the piston is under less pressure than the gas located at a distance from the moving piston; during compression, on the contrary, its pressure near the piston is higher.
Therefore, the state of the gas in this case is considered nonequilibrium (in its volume the parameters or the parameter varies in size). For the same reason, the gas will be nonequilibrium if heat is supplied to the cylinder, since the temperature of the gas layers located next to the heated walls of the cylinder will be higher than the temperature of the layers distant from the walls.
Each equilibrium state of the system can be represented in the coordinate system by one single point, characterizing the constancy of all parameters.
The sequence of changes in the thermodynamic state of a system is called a thermodynamic process. The thermodynamic process is generally accompanied by a change in all or some parameters of the gas system.
If the change in gas parameters over time occurs very slowly, then their difference in different parts systems during the process can be neglected. Such a transition of a system from one state to another can be conventionally considered to consist of a continuous series of equilibrium states, i.e., an equilibrium thermodynamic process.
It is obvious that when a gas transitions from one state to another at a finite speed, the equality of the gas parameters will not be observed, and such a process is not an equilibrium one.
Thermodynamic processes can be reversible And irreversible.
Reversible is an equilibrium process that flows in the forward and reverse directions through the same series of equilibrium states, without causing changes in the system itself and the bodies surrounding the system. That is, as a result of a reversible process, the parameters of the gas system change for the first half of the time according to a certain pattern, and for the second half of the time they return to the initial state strictly along the reverse “path”.
Nonequilibrium processes do not comply with the above conditions, i.e. they are irreversible.
All real processes considered by thermal engineering are irreversible, that is, a reversible process is an idealized model.
Gas work
The gas in the vessel at high blood pressure seeks to expand, that is, to increase its volume. This tendency can be hindered by external forces acting on the gas. Obviously, if a gas, despite external force resistance, manages to expand, then it does work to overcome these external forces.
Similarly, when compressing a gas contained in a vessel, work has to be done to overcome the gas pressure.
Let's try to determine the work described above performed by gas or external forces. Suppose that a certain amount of gas is in a cylinder under a piston sliding without friction, and to which an external force is applied. In the initial state, the system is balanced - the force acting on the piston is balanced by the gas pressure, and the piston remains motionless.
Let, as a result of the supply of heat, the gas expand so that its pressure remains unchanged, and the piston moves upward a certain distance Δh. In this case, the gas performed work equal to the product of the force and the distance traveled.
Knowing the gas pressure p (which remains unchanged during the process) and the area of the piston S, we can determine the force acting on the piston from the gas side: F = pS, and the work done by the gas will be equal to
ΔA = FΔh = pSΔh.
But the product SΔh is an elementary change in the volume ΔV occupied by the gas. Thus, we can write that the work done by a gas depends on the change in its volume:
ΔA = FΔh = pSΔh = pΔV.
If we depict graphically in a coordinate system the transition of a gas from one state to another in the form of a curved line, then each point of this curve will correspond to certain parameters p i Vi .
By dividing this curve into elementary sections, we can conditionally assume that in each section the pressure remains unchanged. Then the gas work in an elementary section will be equal to ΔA = pΔV.
Infinitely narrowing the areas, we move on to the differential expression: dA = pdV.
From this expression it follows that when the gas expands (dV > 0), work is done to overcome external forces, and it is positive. If the gas is compressed by external forces (dV< 0
), работа газа отрицательна. В рассмотренной системе мы рассматривали давление, как неизменный параметр. Для того, чтобы определить полную работу газа при переменном давлении, изменяющемуся по функциональной зависимости p = f(V)
, необходимо провести суммирование элементарных работ.
In this case:
A = Σ pdV or A = ∫ pdV in the range from V 1 to V 2.
Graphically, the work on the diagram p, V is depicted by the surface area between the curve p = f(V) and the abscissas V 1 and V 2 (see Fig. 1).
As can be understood from the graph, the work of a gas to overcome external forces depends not only on the initial and final states, but also on the path along which the process occurred. If the curve p = f(V) has a different shape (more curved, flatter, etc.), then the size of the area enclosed between this curve and the abscissa axis will also change.
In the SI system of units, a unit of work is taken to be Joule(J) . It is allowed to use a non-systemic unit - kilowatt×hour(kWh) which is equal to 3.6 MJ.
Internal energy of gas
Each molecule of a real gas has kinetic energy due to continuous chaotic (Brownian) motion, as well as potential energy due to interaction with neighboring molecules (forces of gravity and electromagnetic interaction).
The sum of the kinetic and potential energy of molecules is called internal energy of gas U. In the general case, the internal energy of a gas depends on its parameters - pressure, volume and temperature, i.e. it is a function of state.
When a system transitions from one state to another, the internal energy changes.
« Physics - 10th grade"
Thermal phenomena can be described using quantities (macroscopic parameters) measured by instruments such as a pressure gauge and thermometer. These devices do not respond to the influence of individual molecules. The theory of thermal processes, which does not take into account the molecular structure of bodies, is called thermodynamics. Thermodynamics considers processes from the point of view of converting heat into other types of energy.
What is internal energy.
What ways of changing internal energy do you know?
Thermodynamics was created in the middle of the 19th century. after the discovery of the law of conservation of energy. It is based on the concept internal energy. The very name “internal” implies consideration of the system as an ensemble of moving and interacting molecules. Let us dwell on the question of what connection exists between thermodynamics and molecular kinetic theory.
Thermodynamics and statistical mechanics.
First scientific theory thermal processes were not based on molecular kinetic theory, but on thermodynamics.
Thermodynamics arose from the study of optimal conditions for using heat to do work. This happened in the middle of the 19th century, long before the molecular kinetic theory received general recognition. At the same time, it was proven that, along with mechanical energy, macroscopic bodies also have energy contained within the bodies themselves.
Nowadays in science and technology, both thermodynamics and molecular-kinetic theory are used to study thermal phenomena. In theoretical physics, molecular kinetic theory is called statistical mechanics
Thermodynamics and statistical mechanics study the same phenomena using different methods and complement each other.
Thermodynamic system called a set of interacting bodies exchanging energy and matter.
Internal energy in molecular kinetic theory.
The main concept in thermodynamics is the concept of internal energy.
Internal body energy(system) is the sum of the kinetic energy of the chaotic thermal motion of molecules and the potential energy of their interaction.
Mechanical energy the body (system) as a whole is not included in the internal energy. For example, the internal energy of gases in two identical vessels under equal conditions is the same, regardless of the movement of the vessels and their location relative to each other.
Calculating the internal energy of a body (or its change), taking into account the movement of individual molecules and their positions relative to each other, is almost impossible due to the huge number of molecules in macroscopic bodies. Therefore, it is necessary to be able to determine the value of internal energy (or its change) depending on macroscopic parameters that can be directly measured.
Internal energy of an ideal monatomic gas.
Let us calculate the internal energy of an ideal monatomic gas.
According to the model, the molecules of an ideal gas do not interact with each other, therefore, the potential energy of their interaction is zero. The entire internal energy of an ideal gas is determined by the kinetic energy of the random motion of its molecules.
To calculate the internal energy of an ideal monatomic gas of mass m, you need to multiply the average kinetic energy of one atom by the number of atoms. Taking into account that kN A = R, we obtain the formula for the internal energy of an ideal gas:
The internal energy of an ideal monatomic gas is directly proportional to its absolute temperature.
It does not depend on the volume and other macroscopic parameters of the system.
Change in internal energy of an ideal gas
i.e., it is determined by the temperatures of the initial and final states of the gas and does not depend on the process.
If an ideal gas consists of more complex molecules than a monatomic one, then its internal energy is also proportional to the absolute temperature, but the proportionality coefficient between U and T is different. This is explained by the fact that complex molecules not only move translationally, but also rotate and oscillate relative to their equilibrium positions. The internal energy of such gases is equal to the sum of the energies of the translational, rotational and vibrational movements of the molecules. Consequently, the internal energy of a polyatomic gas is greater than the energy of a monatomic gas at the same temperature.
Dependence of internal energy on macroscopic parameters.
We have established that the internal energy of an ideal gas depends on one parameter - temperature.
In real gases, liquids and solids, the average potential energy of interaction between molecules is not equal to zero. True, for gases it is much less than the average kinetic energy of molecules, but for solids and liquids it is comparable to it.
The average potential energy of interaction between gas molecules depends on the volume of the substance, since when the volume changes, the average distance between the molecules changes. Consequently, the internal energy of a real gas in thermodynamics in the general case depends, along with the temperature T, and on the volume V.
Is it possible to say that the internal energy of a real gas depends on pressure, based on the fact that pressure can be expressed in terms of temperature and volume of the gas.
The values of macroscopic parameters (temperature T of volume V, etc.) unambiguously determine the state of bodies. Therefore, they also determine the internal energy of macroscopic bodies.
The internal energy U of macroscopic bodies is uniquely determined by the parameters characterizing the state of these bodies: temperature and volume.
To calculate the internal energy of an ideal monatomic gas mass, you need to multiply the average kinetic energy of one atom by the number of atoms. Considering that , we obtain the value of the internal energy of an ideal gas:
If an ideal gas consists of more complex molecules than a monatomic gas, then its internal energy is equal to the sum of the translational and rotational motion of the molecules.
For diatomic gas:
For polyatomic gas:
In real gases, liquids and solids, the average potential energy of interaction between molecules is not zero. For gases it is much less than the average kinetic energy of molecules, but for solids and liquids it is comparable to it. The average potential energy of interaction between molecules depends on the volume of the substance, since when the volume changes, the average distance between the molecules changes. Hence, In the general case, internal energy in thermodynamics, along with temperature, also depends on volume.
Quantity of heat:
The process of transferring energy from one body to another without doing work is called heat exchange or heat transfer. Heat exchange occurs between bodies having different temperatures. When contact is established between bodies with different temperatures, part of the internal energy is transferred from a body with a higher temperature to a body with a lower temperature. The energy transferred to a body as a result of heat exchange is called amount of heat.
Specific heat capacity of a substance:
If the heat transfer process is not accompanied by work, then, based on the first law of thermodynamics, the amount of heat is equal to the change in the internal energy of the body: .
The average energy of the random translational motion of molecules is proportional to the absolute temperature. The change in the internal energy of a body is equal to the algebraic sum of the changes in the energy of all atoms or molecules, the number of which is proportional to the mass of the body, therefore the change in internal energy and, therefore, the amount of heat is proportional to the mass and the change in temperature:
The proportionality factor in this equation is called specific heat capacity of a substance. Specific heat capacity shows how much heat is needed to heat 1 kg of a substance by 1 K.
Work in thermodynamics:
In mechanics, work is defined as the product of the moduli of force and displacement and the cosine of the angle between them. Work is done when a force acts on a moving body and is equal to the change in its kinetic energy.
In thermodynamics, the movement of a body as a whole is not considered; we are talking about the movement of parts of a macroscopic body relative to each other. As a result, the volume of the body changes, but its speed remains equal to zero. Work in thermodynamics is defined in the same way as in mechanics, but is equal to the change not in the kinetic energy of the body, but in its internal energy.
When work is performed (compression or expansion), the internal energy of the gas changes. The reason for this is: during elastic collisions of gas molecules with a moving piston, their kinetic energy changes.
Let us calculate the work done by the gas during expansion. The gas acts on the piston with a force where is the gas pressure and is the surface area of the piston. When gas expands, the piston moves in the direction of the force a small distance. If the distance is small, then the gas pressure can be considered constant. The work done by the gas is:
Where is the change in gas volume.
In the process of gas expansion, it does positive work, since the direction of the force and displacement coincide. During the expansion process, the gas releases energy to surrounding bodies.
The work done by external bodies on the gas differs from the work of the gas only in sign, since the force acting on the gas is opposite to the force with which the gas acts on the piston and is equal to it in absolute value (Newton’s third law); and the movement remains the same. Therefore, the work of external forces is equal to:
First law of thermodynamics:
The first law of thermodynamics is the law of conservation of energy, extended to thermal phenomena. Law of energy conservation: Energy in nature does not arise from nothing and does not disappear: the amount of energy is unchanged, it only passes from one form to another.
Thermodynamics considers bodies whose center of gravity remains virtually unchanged. The mechanical energy of such bodies remains constant, and only the internal energy can change.
Internal energy can change in two ways: heat transfer and work. In the general case, internal energy changes both due to heat transfer and due to work done. The first law of thermodynamics is formulated precisely for such general cases:
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:
If the system is isolated, then no work is done on it and it does not exchange heat with surrounding bodies. According to the first law of thermodynamics the internal energy of an isolated system remains unchanged.
Considering that , the first law of thermodynamics can be written as follows:
The amount of heat transferred to the system goes to change its internal energy and to perform work on external bodies by the system.
Second law of thermodynamics: It is impossible to transfer heat from a colder system to a hotter one in the absence of other simultaneous changes in both systems or in surrounding bodies.
Application of the first law of thermodynamics to isoprocesses:
At isochoric process The volume of the gas does not change and therefore the work done by the gas is zero. The change in internal energy is equal to the amount of heat transferred:
At isothermal process The internal energy of an ideal gas does not change. The entire amount of heat transferred to the gas is used to perform work:
At isobaric process The amount of heat transferred to the gas goes to change its internal energy and to perform work at constant pressure.
Adiabatic process:
Adiabatic process– process in a thermally insulated system. Consequently, the change in internal energy during an adiabatic process occurs only due to the performance of work:
Since the work of external forces during compression is positive, the internal energy of a gas during adiabatic compression increases, and its temperature rises.
During adiabatic expansion, the gas does work by reducing its internal energy, so the temperature of the gas decreases during adiabatic expansion.
Operating principle of heat engines:
A heat engine is an engine that produces mechanical work using the energy released during the combustion of fuel. Some types of heat engines:
Steam engine;
Steam turbine;
Internal combustion engine;
Jet engine.
The physical principles of operation of all heat engines are the same. A heat engine consists of three main parts: a heater, a working fluid, and a refrigerator.
The operating process of a heat engine: The working fluid is brought into contact with the heater ( - high), so the working fluid receives from the heater. Due to this amount of heat, the working fluid performs mechanical work. Then the working fluid is brought into contact with the refrigerator ( - low), so the working fluid gives off heat to the refrigerator. Thus it returns to its original state. Now the working fluid is brought into contact with the heater and everything happens all over again. Consequently, a heat engine is of periodic action, that is, in this machine the body undergoes a closed process - a cycle. During each cycle, the working fluid does work.
Efficiency is usually expressed as a percentage:
Heat engine efficiency and its maximum value:
At the beginning of the 19th century, French engineer Sadi Carnot explored ways to increase the efficiency of heat engines. He came up with a cycle that should perform an ideal gas in a certain heat engine, such that the highest possible efficiency is obtained. The Carnot cycle consists of two isotherms and two adiabats.
An ideal gas is brought into contact with a heater and allowed to expand isothermally, that is, at the temperature of the heater. When the expanded gas goes into state 2, it is thermally insulated from the heater and given the opportunity to expand adiabatically, that is, the gas does work due to the decrease in its internal energy. Expanding adiabatically, the gas cools until its temperature is equal to the temperature of the refrigerator (state 3). The gas is now brought into contact with the refrigerator and compressed isothermally. The gas releases to the refrigerator. The gas enters state 4. The gas is then thermally insulated from the refrigerator and compressed adiabatically. In this case, the gas temperature increases and reaches the temperature of the heater. The process is repeated from the beginning.
(*) - formula for calculating the efficiency of an ideal heat engine operating according to the Carnot cycle with an ideal gas.
Carnot showed that the efficiency of any other heat engine (that is, with a different working fluid or operating on a different cycle) will be less than the efficiency of the Carnot cycle. In practice, machines operating on the Carnot cycle are not used, but formula (*) allows one to determine the maximum efficiency at given temperatures of the heater and refrigerator.
Obviously, to increase efficiency, you need to lower the temperature of the refrigerator and increase the temperature of the heater. It is not profitable to artificially lower the temperature of the refrigerator, since this requires additional energy consumption. The temperature of the heater can also be increased to a certain limit, since various materials have different heat resistance at high temperatures. However, the Carnot formula showed that there are untapped reserves for increasing efficiency, since the practical efficiency is very different from the efficiency of the Carnot cycle.
Heat engines and nature conservation:
Evaporation and condensation, saturated and unsaturated vapors:
The uneven distribution of kinetic energy of thermal motion of molecules leads to the fact that at any temperature the kinetic energy of some molecules of a liquid or solid may exceed the potential energy of their connection with other molecules. Evaporation is a process in which molecules are emitted from the surface of a liquid or solid whose kinetic energy exceeds the potential energy of interaction between the molecules. Evaporation is accompanied by cooling of the liquid, since molecules with high kinetic energy leave the liquid, and the internal energy of the liquid decreases. The ejected molecules begin to move randomly in the thermal motion of the gas; they can either be permanently removed from the surface of the liquid, or return to the liquid again. This process is called condensation.
The evaporation of a liquid in a closed vessel at a constant temperature leads to a gradual increase in the concentration of molecules of the evaporating substance in the gaseous state. Some time after the start of the evaporation process, the concentration of the substance in the gaseous state reaches a value at which the number of molecules returning to the liquid per unit time becomes equal to the number of molecules leaving the surface of the liquid during the same time. A dynamic equilibrium is established between the processes of evaporation and condensation of the substance.
A substance in a gaseous state that is in dynamic equilibrium with a liquid is called saturated steam. Steam at a pressure below the saturated vapor pressure is called unsaturated.
When saturated steam is compressed, the concentration of steam molecules increases, the balance between the processes of evaporation and condensation is disrupted and part of the steam turns into liquid. As saturated steam expands, the concentration of its molecules decreases and part of the liquid turns into steam. Thus, the saturated vapor concentration remains constant regardless of volume. Since gas pressure is proportional to concentration and temperature (), the pressure of saturated vapor at a constant temperature does not depend on volume.
The intensity of the evaporation process increases with increasing liquid temperature. Therefore, the dynamic equilibrium between evaporation and condensation with increasing temperature is established at high concentrations of gas molecules.
The pressure of an ideal gas at a constant concentration of molecules increases in direct proportion to the absolute temperature. Since the concentration of molecules in saturated steam increases with increasing temperature, the pressure of saturated steam increases faster with increasing temperature than the pressure of an ideal gas with a constant concentration of molecules. That is the saturated vapor pressure increases not only due to an increase in the temperature of the liquid, but also due to an increase in the concentration of vapor molecules.
The main difference in the behavior of an ideal gas and saturated steam is that when the temperature of the steam in a closed vessel changes (or when the volume changes at a constant temperature), the mass of the steam changes.
Dependence of the boiling point of a liquid on pressure:
As the temperature increases, the rate of evaporation of the liquid increases, and at a certain temperature the liquid begins to boil. When boiling, rapidly growing vapor bubbles are formed throughout the entire volume of the liquid, which float to the surface. The boiling point of the liquid remains constant.
Liquids always contain dissolved gases, which are released at the bottom and walls of the vessel. The liquid vapors inside the bubbles are saturated. As the temperature increases, the saturated vapor pressure increases and the bubbles increase in size. Under the influence of buoyant force they float to the surface.
The dependence of saturated vapor pressure on temperature explains why the boiling point of a liquid depends on the pressure on its surface. A vapor bubble can grow when the pressure of the saturated vapor inside it slightly exceeds the pressure in the liquid, which is the sum of the air pressure on the surface of the liquid (external pressure) and the hydrostatic pressure of the liquid column.
Boiling begins at the temperature at which the saturated vapor pressure in the bubbles is equal to the pressure in the liquid. The greater the external pressure, the higher the boiling point.
Each liquid has its own boiling point, which depends on the saturated vapor pressure. the higher the saturated vapor pressure, the lower the boiling point of the corresponding liquid, since at lower temperatures the saturated vapor pressure becomes equal to atmospheric pressure.
As the temperature of the liquid increases, the saturated vapor pressure increases and at the same time its density increases. The density of a liquid in equilibrium with its vapor, on the contrary, decreases due to the expansion of the liquid when heated.
If in one figure we draw curves of the dependence of the density of a liquid and the density of its saturated vapor on temperature, then for the liquid the curve will go down, and for the vapor it will go up.
At a certain temperature, both curves merge, that is, the density of the liquid becomes equal to the density of the vapor.
Critical temperature is the temperature at which the differences in physical properties between a liquid and its saturated vapor disappear.
At temperatures above critical, the substance does not turn into liquid under any pressure.
Air humidity:
Atmospheric air is a mixture of various gases and water vapor. Each of the gases contributes to the total pressure produced by the air on the bodies in it.
The pressure that water vapor would produce if all other gases were absent is called the partial pressure of water vapor.
Relative air humidity is the ratio of the partial pressure of water vapor contained in the air at a given temperature to the saturated vapor pressure at the same temperature, expressed as a percentage:
Since the pressure of saturated vapor is lower, the lower the temperature, when the air is cooled, the water vapor in it becomes saturated at a certain temperature. The temperature at which water vapor in the air becomes saturated is called dew point.
The dew point can be used to find the water vapor pressure in the air. It is equal to the saturated vapor pressure at a temperature equal to the dew point. Based on the vapor pressure in the air and the saturated vapor pressure at a given temperature, the relative humidity of the air can be determined.
Crystalline and amorphous solids:
Amorphous are bodies whose physical properties are the same in all directions. Amorphous bodies are isotropic– they do not have a strict order in the arrangement of atoms. Examples of amorphous bodies include pieces of hardened resin, amber, and glass.
Solids in which atoms or molecules are arranged in an orderly manner and form a periodically repeating internal structure are called crystals. The physical properties of crystalline bodies are not the same in different directions, but the same in parallel directions. This property of crystals is called anisotropy.
The anisotropy of the mechanical, thermal, electrical and optical properties of crystals is explained by the fact that with an ordered arrangement of atoms, molecules or ions, the interaction forces between them and the interatomic distances are unequal in different directions.
Crystalline bodies are divided into single crystals And polycrystals. Single crystals sometimes have geometrically correct form, But main feature single crystal - a periodically repeating internal structure throughout its entire volume. A polycrystalline body is a collection of chaotically oriented small crystals – crystallites – fused with each other. Each small single crystal of a polycrystalline body is anisotropic, but the polycrystalline body is isotropic.
Mechanical properties of solids:
Let us consider the mechanical properties of a solid using tensile deformation as an example. In any section of a deformed body, elastic forces act, preventing the body from breaking into pieces. Mechanical stress is the ratio of the modulus of elastic force to the cross-sectional area of the body:
At small deformations, the stress is directly proportional to the relative elongation (section OA). This dependency is called Hooke's law:
Where is Young's modulus.
Let us denote then
Hooke's law is satisfied only for small deformations, and therefore, for stresses not exceeding a certain limit. The maximum voltage at which Hooke's law is still satisfied is called limit of proportionality.
If you increase the load, the deformation becomes nonlinear; the stress ceases to be directly proportional to the relative elongation. However, with small nonlinear deformations, after removing the load, the shape and size of the body are practically restored (section AB). The maximum stress at which noticeable residual deformations do not yet occur (relative residual deformation does not exceed 0.1%) is called elastic limit .
If the external load is such that the stress in the material exceeds the elastic limit, then after the load is removed the body remains deformed. At a certain voltage value corresponding to point C on the diagram, the elongation increases practically without increasing the load. This phenomenon is called fluidity of the material(CD section).
Further, with increasing deformation, the stress curve begins to increase slightly and reaches a maximum at point E. Then the stress drops sharply and the body collapses. The rupture occurs after the stress reaches a maximum value called tensile strength.
Elastic deformations:
At elastic deformations the size and shape of the body are restored when the load is removed.
