System bodies or simply a system is the collection of bodies under consideration. An example of a system is a liquid and vapor in equilibrium with it. In particular, the system can consist of one body.
Any system can be in different states, differing in temperature, pressure, volume, etc. Such quantities characterizing the state of the system are called state parameters.
Not always any parameter has a specific value. If, for example, the temperature at different points of the body is not the same, then the body cannot be assigned a certain value of the parameter T. In this case state called nonequilibrium. If such a body is isolated from other bodies and left to itself, then the temperature will take the same value T for all points - the body will go into an equilibrium state. This value of T does not change until the body is removed from the equilibrium state by an external influence.
The same may occur for other parameters, for example, pressure p. If you take a gas enclosed in a cylindrical vessel, closed with a tightly fitting piston, and begin to quickly move the piston, then a gas cushion will form under it, the pressure in which will be greater than in the rest of the gas volume. Consequently, the gas in this case cannot be characterized by a certain pressure value p and its state will be nonequilibrium. However, if you stop moving the piston, the pressure at different points in the volume will equalize and the gas will go into an equilibrium state.
So, equilibrium state of the system is a state in which all parameters of the system have certain values that remain constant under constant external conditions for an arbitrarily long time.
If we plot the values of any two parameters along the coordinate axes, then any equilibrium state of the system can be represented by a point on this graph
(see, for example, point 1 in Fig. 212). A nonequilibrium state cannot be depicted in this way, because at least one of the parameters will not have a certain value in a nonequilibrium state.
Every process, i.e., the transition of a system from one state to another, is associated with an imbalance of the system. Consequently, when any process occurs in a system, it passes through a sequence of nonequilibrium states. Referring to the already considered process of gas compression in a vessel closed by a piston, we can conclude that the imbalance when moving the piston is more significant, the faster the gas is compressed. If you move the piston very slowly, then the equilibrium is slightly disturbed and the pressure at different points differs little from some average value p. In the limit, if gas compression occurs infinitely slowly, the gas at each moment of time will be characterized by a certain pressure value. Consequently, in this case, the state of the gas at each moment of time is equilibrium and an infinitely slow process will consist of a sequence of equilibrium states.
Process consisting of a continuous sequence of equilibrium states is called equilibrium . From the above it follows that only an infinitely slow process can be equilibrium, therefore the equilibrium process is an abstraction.
The equilibrium process can be depicted on the graph of the corresponding curve (Fig.). Nonequilibrium processes are conventionally depicted by dotted curves.
The concepts of equilibrium state and equilibrium process play an important role in thermodynamics. All quantitative conclusions of thermodynamics are strictly applicable only to equilibrium processes.
We will call a system of bodies or simply a system the totality of the bodies under consideration. An example of a system is a liquid and vapor in equilibrium with it. In particular, the system can consist of one body.
Any system can be in different states, differing in temperature, pressure, volume, etc. Such quantities that characterize the state of the system are called state parameters.
Not always any parameter has a specific value. If, for example, the temperature at different points of the body is not the same, then a certain value of the parameter T cannot be assigned to the body. In this case, the state is called nonequilibrium. If such a body is isolated from other bodies and left to itself, then the temperature will equalize and take the same value T for all points - the body will go into an equilibrium state. This value of T does not change until the body is removed from the equilibrium state by an external influence.
The same may be true for other parameters, such as pressure. If you take a gas enclosed in a cylindrical vessel, closed with a tightly fitting piston, and begin to quickly move the piston, then a gas cushion will form under it, the pressure in which will be greater than in the rest of the gas volume. Consequently, the gas in this case cannot be characterized by a certain pressure value, and its state will be nonequilibrium. However, if you stop moving the piston, the pressure at different points in the volume will equalize and the gas will go into an equilibrium state.
The process of transition of a system from a nonequilibrium state to an equilibrium state is called the relaxation process or simply relaxation. The time spent on such a transition is called relaxation time. The relaxation time is taken to be the time during which the initial deviation of any value from the equilibrium value decreases by a factor. Each system parameter has its own relaxation time. The longest of these times plays the role of the relaxation time of the system.
So, the equilibrium state of a system is a state in which all the parameters of the system have certain values that remain constant under constant external conditions for an arbitrarily long time.
If we plot the values of any two parameters along the coordinate axes, then any equilibrium state of the system can be represented by a point on the coordinate plane (see, for example, point 1 in Fig. 81.1). A nonequilibrium state cannot be depicted in this way, because at least one of the parameters will not have a certain value in a nonequilibrium state.
Any process, i.e., the transition of a system from one state to another, is associated with a violation of the equilibrium of the system. Consequently, when any process occurs in a system, it passes through a sequence of nonequilibrium states. Referring to the already considered process of gas compression in a vessel closed by a piston, we can conclude that the imbalance when moving the piston is more significant, the faster the gas is compressed. If you move the piston very slowly, then the equilibrium is slightly disturbed and the pressure at different points differs little from some average value. In the limit, if gas compression occurs infinitely slowly, the gas at each moment of time will be characterized by a certain pressure value. Consequently, in this case, the state of the gas at each moment of time is equilibrium, and an infinitely slow process will consist of a sequence of equilibrium states.
A process consisting of a continuous sequence of equilibrium states is called equilibrium or quasi-static. From the above it follows that only an infinitely slow process can be equilibrium.
If they occur sufficiently slowly, real processes can approach the equilibrium as close as desired.
The equilibrium process can be carried out in the opposite direction, and the system will go through the same states as during the forward process, but in the reverse order. Therefore, equilibrium processes are also called reversible.
A reversible (i.e., equilibrium) process can be depicted on the coordinate plane of the corresponding curve (see Fig. 81.1). We will conventionally depict irreversible (i.e. nonequilibrium) processes with dotted curves.
The process in which a system, after a series of changes, returns to its original state is called a circular process or cycle. Graphically, the cycle is represented by a closed curve.
The concepts of equilibrium state and reversible process play an important role in thermodynamics. All quantitative conclusions of thermodynamics are strictly applicable only to equilibrium states and reversible processes.
Systematic approach to modeling
Concept of the system. The world around us consists of many different objects, each of which has various properties, and at the same time the objects interact with each other. For example, objects such as the planets of our solar system have different properties (mass, geometric dimensions, etc.) and, according to the law of universal gravitation, interact with the Sun and with each other.
The planets are part of a larger object - the Solar System, and the Solar System is part of our Milky Way galaxy. On the other hand, planets are made up of atoms of various chemical elements, and atoms are made up of elementary particles. We can conclude that almost every object consists of other objects, that is, it represents system.
An important feature of the system is its holistic functioning. A system is not a set of individual elements, but a collection of interconnected elements. For example, a computer is a system consisting of various devices, and the devices are interconnected both hardware (physically connected to each other) and functionally (information is exchanged between devices).
System is a collection of interconnected objects called system elements.
The state of the system is characterized by its structure, that is, the composition and properties of the elements, their relationships and connections with each other. The system maintains its integrity under the influence of various external influences and internal changes as long as it maintains its structure unchanged. If the structure of the system changes (for example, one of the elements is removed), then the system may cease to function as a whole. So, if you remove one of the computer devices (for example, a processor), the computer will fail, that is, it will cease to exist as a system.
Static information models. Any system exists in space and time. At each moment of time, the system is in a certain state, which is characterized by the composition of the elements, the values of their properties, the magnitude and nature of the interaction between the elements, and so on.
Thus, the state of the Solar system at any moment in time is characterized by the composition of the objects included in it (the Sun, planets, etc.), their properties (size, position in space, etc.), the magnitude and nature of the interaction with each other (gravitational forces, with the help of electromagnetic waves, etc.).
Models that describe the state of a system at a certain point in time are called static information models.
In physics, examples of static information models are models that describe simple mechanisms, in biology - models of the structure of plants and animals, in chemistry - models of the structure of molecules and crystal lattices, and so on.
Dynamic information models. The state of systems changes over time, that is, processes of change and development of systems. So, the planets move, their position relative to the Sun and each other changes; The Sun, like any other star, develops, its chemical composition, radiation, and so on change.
Models that describe the processes of change and development of systems are called dynamic information models.
In physics, dynamic information models describe the movement of bodies, in biology - the development of organisms or animal populations, in chemistry - the processes of chemical reactions, and so on.
Questions to Consider
1. Do computer components form a system: Before assembly? After assembly? After turning on the computer?
2. What is the difference between static and dynamic information models? Give examples of static and dynamic information models.
State. The concept of state usually characterizes an instant photograph, a “slice” of the system, a stop in its development. It is determined either through input influences and output signals (results), or through properties, parameters of the system (for example, pressure, speed, acceleration - for physical systems; productivity, cost of production, profit - for economic systems).
Thus, a state is a set of essential properties that a system possesses at a given moment in time.
Possible states of a real system form the set of admissible system states.
The number of states (the power of a set of states) can be finite, countable (the number of states is measured discretely, but their number is infinite); power continuum (states change continuously and their number is infinite and uncountable).
States can be described through state variables. If the variables are discrete, then the number of states can be either finite or countable. If the variables are analog (continuous), then the power is continuum.
The minimum number of variables through which a state can be specified is called phase space. Changes in the state of the system are displayed in phase space phase trajectory.
Behavior. If a system is capable of transitioning from one state to another (for example, s 1 →s 2 →s 3 → ...), then they say that it has behavior. This concept is used when the patterns (rules) of transition from one state to another are unknown. Then they say that the system has some behavior and find out its nature.
Equilibrium. The ability of a system in the absence of external disturbing influences (or with constant influences) to maintain its state for an indefinitely long time. This state is called a state of equilibrium.
Sustainability. The ability of a system to return to a state of equilibrium after it has been removed from this state under the influence of external (and in systems with active elements - internal) disturbing influences.
The state of equilibrium to which the system is capable of returning is called a stable state of equilibrium.
Development. Development is usually understood as an increase in the complexity of a system, an improvement in adaptability to external conditions. As a result, a new quality or state of the object arises.
It is advisable to distinguish a special class of developing (self-organizing) systems that have special properties and require the use of special approaches to their modeling.
System inputsx i- these are various points of influence of the external environment on the system (Fig. 1.3).
The inputs of the system can be information, matter, energy, etc., which are subject to transformation.
Generalized input ( X) name some (any) state of all r system inputs, which can be represented as a vector
X = (x 1 , x 2 , x 3 , …, x k, …, x r).
System outputsy i- these are various points of influence of the system on the external environment (Fig. 1.3).
The output of the system is the result of the transformation of information, matter and energy.
Movement of the system is a process of consistent change in its state.
Let us consider the dependences of the system states on the functions (states) of the system inputs, its states (transitions) and outputs.
State of the system Z(t) at any time t depends on the function of the inputs X(t), as well as from its previous states at moments (t– 1), (t– 2), ..., i.e. from the functions of its states (transitions)
Z(t) = F c , (1)
Where Fc– function of the state (transitions) of the system.
Relationship between input function X(t) and exit function Y(t) systems, without taking into account previous states, can be represented in the form
Y(t) = Fв [X(t)],
Where F in– function of system outputs.
A system with such an output function is called static.
If the system output depends not only on the functions of the inputs X(t), but also on functions of states (transitions) Z( t – 1), Z(t– 2), ..., then
systems with such an output function are called dynamic(or systems with behavior).
Depending on the mathematical properties of the functions of inputs and outputs of systems, discrete and continuous systems are distinguished.
For continuous systems, expressions (1) and (2) look like:
(4)
Equation (3) determines the state of the system and is called the equation of system states.
Equation (4) determines the observed output of the system and is called the observational equation.
Functions Fc(function of system states) and F in(output function) take into account not only the current state Z(t), but also previous states Z(t – 1), Z(t – 2), …, Z(t – v) systems.
Previous states are a parameter of the system's "memory". Therefore, the value v characterizes the volume (depth) of system memory.
System processes is a set of successive changes in the state of the system to achieve a goal. System processes include:
– input process;
– output process;
Quantities characterizing the state of the system , such as temperature, pressure, volume, etc., we will call state parameters .
We will call the state of the system nonequilibrium , if at least one of the state parameters cannot be assigned a specific value .
If all parameters of the system state have certain values that remain constant under fixed external conditions for an arbitrarily long time, then the state of the system is called equilibrium .
The concept " certain values " implies that the parameter value is the same at all points of the system under consideration . For example, the temperature in the classroom, strictly speaking, is different at different points, which means has no specific meaning . It is unacceptable to take the average value as a definite value. If the room is isolated from external influences, then, after some time, the temperature at all its points will level out, and then it will be possible to talk about a certain temperature value in the room. Similar ideas apply to pressure, density and other parameters of the state of the system.
Transition system from one state to another is called process .
It is obvious that during any process the system passes through a sequence of nonequilibrium states. However, the slower the process is, the closer the states of the system during the process are to equilibrium. In the limit, if the process proceeds infinitely slowly, i.e., it is quasi-static, we can assume that at any given moment the state of the system is equilibrium.
A-priory equilibrium called process consisting of a continuous sequence of equilibrium states . It's obvious that Only a quasi-static process can be equilibrium.
An important feature of equilibrium processes is that they can be carried out in reverse direction, i.e. from the end to the beginning through a reverse sequence of states, and as a result of the direct and reverse processes, no changes will occur in the system and surrounding bodies. Therefore, processes that have this property - and they can only be equilibrium processes - are also called reversible .
Terms quasi-static, equilibrium and reversible in relation to thermodynamic processes, they are essentially synonyms, but each of them emphasizes its own essential feature of the process being described.
Experience shows that a system isolated from external influences makes a transition from a nonequilibrium to an equilibrium state. This process is called relaxation system, and its duration is relaxation time .
Distinguish circular process s or cycles , as a result of which the system returns to its original state.
On graphs, equilibrium processes are depicted as curves. In general, nonequilibrium processes cannot be represented by curves, since the parameters do not have a definite value.
We also note that, strictly saying quantitative conclusions of thermodynamics apply only to equilibrium states and reversible processes . However, in a huge number of cases, real processes, which are by no means equilibrium, are described with very high accuracy by the laws of thermodynamics.