Physics
Thermal Equilibrium
Thermal equilibrium refers to a state in which two or more objects or systems are at the same temperature and there is no net flow of heat between them. In this state, the thermal energy is evenly distributed, and there is no change in temperature over time. It is a key concept in understanding heat transfer and the behavior of systems in thermal contact.
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10 Key excerpts on "Thermal Equilibrium"
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
Differences in temperature maintain the transfer of heat, or heat transfer, throughout the universe. Heat transfer is the movement of energy from one place or material to another as a result of a difference in temperature. (You will learn more about heat transfer later in this chapter.) Thermal Equilibrium An important concept related to temperature is Thermal Equilibrium. Two objects are in Thermal Equilibrium if they are in close contact that allows either to gain energy from the other, but nevertheless, no net energy is transferred between them. Even when not in contact, they are in Thermal Equilibrium if, when they are placed in contact, no net energy is transferred between them. If two objects remain in contact for a long time, they typically come to equilibrium. In other words, two objects in Thermal Equilibrium do not exchange energy. Experimentally, if object A is in equilibrium with object B, and object B is in equilibrium with object C, then (as you may have already guessed) object A is in equilibrium with object C. That statement of transitivity is called the zeroth law of thermodynamics. (The number “zeroth” was suggested by British physicist Ralph Fowler in the 1930s. The first, second, and third laws of thermodynamics were already named and numbered then. The zeroth law had seldom been stated, but it needs to be discussed before the others, so Fowler gave it a smaller number.) Consider the case where A is a thermometer. The zeroth law tells us that if A reads a certain temperature when in equilibrium with B, and it is then placed in contact with C, it will not exchange energy with C; therefore, its temperature reading will remain the same (Figure 1.2). In other words, if two objects are in Thermal Equilibrium, they have the same temperature. Figure 1.2 If thermometer A is in Thermal Equilibrium with object B, and B is in Thermal Equilibrium with C, then A is in Thermal Equilibrium with C.
- Kevin Dahm, Donald Visco(Authors)
- 2014(Publication Date)
- Cengage Learning EMEA(Publisher)
1.4.8 Temperature Internal energy was described in Section 1.4.6 as microscopic kinetic and potential energy; the energy of individual molecules. A difficulty is that microscopic potential and kinetic energy is not something that can be measured directly. The virtue of temperature is that it is a readily measurable property that allows us to benchmark the internal energy of a system. The Celsius temperature scale was originally defined as The freezing point of water at atmospheric pressure is 0°C. The boiling point of water at atmospheric pressure is 100°C. The phenomenon of heat transfer is what makes a temperature scale mean-ingful. Two objects are said to be in “Thermal Equilibrium” if no heat is transferred between them, even though they are in contact such that heat transfer could occur. By definition, materials in Thermal Equilibrium are said to be at the same tem-perature. Thermal Equilibrium has been observed to be transitive; that is, if mate-rial A is in Thermal Equilibrium with material B, then any other material that is in Thermal Equilibrium with material A will also be in Thermal Equilibrium with material B. Thus, any material that is in Thermal Equilibrium with water at its normal freez-ing point is said to have a temperature of 273.15 K. Any material that would transfer heat TO water at its normal freezing point has a temperature higher than 273.15 K, and any material to which heat would transfer FROM water at its normal freezing point has a temperature lower than 273.15 K. The definition of two points permits construction of a linear scale for temperature in between these two points. The tran-sitive nature of Thermal Equilibrium allows us to calibrate instruments that measure temperature (e.g., we know that any two objects that provide the same reading on a thermometer will be in Thermal Equilibrium with each other). While temperature is related to internal energy, it is not a simple or linear rela-tionship.
eBook - PDF- Robert DeHoff(Author)
- 2006(Publication Date)
- CRC Press(Publisher)
Once the system has found the position in space O which achieves this balance, it will remain fixed in that position until one of the weights is changed. Furthermore, if the system is displaced from its equilibrium position, e.g., if the body is moved to any position in the neighborhood of O , it will return to O . In thermodynamics, the influences that operate to modify the condition of a system are more general than mechanical forces. Nonetheless, the intuitive notion of an equilibrium condition also applies to such systems. This idea of an equilibrium state has two components: 1. It is a state of rest. 2. It is a state of balance. The first component means that the condition of the system, no matter what it might be, is time independent. The system has achieved a stationary state. No changes can occur in a system that has come to equilibrium except by the action of influences that originate outside the system/surroundings complex. The second component to the concept means that if the system is perturbed from its equilibrium condition by some outside influence, it will return again to the same condition when it again comes to rest. 5.2 THERMODYNAMIC FORMULATION OF A GENERAL CRITERION FOR EQUILIBRIUM Systems can experience two distinct classes of conditions that are time invariant, i.e., two classes of stationary states. Either the system is in an equilibrium state or it has achieved a steady state. A simple example of a steady state is shown in Figure 5.2. A copper rod is surrounded by an insulating jacket except at its ends. One end is placed in contact with a furnace maintained at temperature T 1 ; the other end contacts a water-cooled plate maintained at temperature T 2 . Heat will flow through the rod from left to right and the temperature profile will evolve with time. Eventually, because the external conditions are fixed, the temperature profile will achieve a distribution that no longer Equilibrium in Thermodynamic Systems 109
eBook - PDF- Wassim M. Haddad(Author)
- 2019(Publication Date)
- Princeton University Press(Publisher)
Any addition or removal of heat is assumed to be sufficiently slow so that each subsystem remains in internal equilibrium. Since subsystems are generally not in equilibrium with each other, there is generally no meaning of “system temperature.” When the subsystems are all at a single common temperature ¯ T , then we say the system is in Thermal Equilibrium with temperature ¯ T . We write ¯ T for the temperature vector of a system in Thermal Equilibrium, that is, ¯ T = e ¯ T . In this section, we distinguish the notion of Thermal Equilibrium , meaning the condition of an isolated system at a uniform temperature, from the notion of dynamic equilibrium , meaning the condition of a dynamic system with time rate of change equal to zero. In classical thermodynamics, energy, entropy, and temperature are related by the fundamental thermodynamic relationship [63, 252]. In the TEMPERATURE EQUIPARTITION AND THE KINETIC THEORY OF GASES 211 absence of mechanical work, this relationship can be written as T i = ∂ S i ∂E i -1 . (4.28) We will define entropy as a function of energy, that is, S i ( E i ) and S ( E ). It is also convenient to write the entropies as functions of temperature, using E i ( T i ). Thus, we define E ( T ) , [ E 1 ( T 1 ) , . . . , E q ( T q )] T , ˜ S i ( T i ) , S i ( E i ( T i )), and ˜ S ( T ) , S ( E ( T )) = ∑ q i =1 ˜ S i ( T i ). Let d Q i be an infinitesimal amount of heat received by subsystem i . Since energy is assumed to be transferred only as heat, d E i = d Q i . The infinitesimal change in entropy that accompanies this heat addition is given by d S i = ∂ S i ∂E i d E i = d Q i T i , (4.29) where subsystem G i is in equilibrium at temperature T i . In terms of heat flow rates, (4.29) can be written as d S i d t = 1 T i d Q i d t = q i T i , (4.30) where q i , ˙ Q i . Here, the time rate of change is assumed to be sufficiently slow so that the system remains in a slowly varying state of equilibrium.
eBook - PDF- Ethirajan Rathakrishnan(Author)
- 2012(Publication Date)
- CRC Press(Publisher)
However, the pressure may vary within the system with elevation as a result of gravitational effects. But the higher pressure at a bottom layer is balanced by the extra weight it must carry, and, therefore, there is no imbalance of forces. Pressure variation as a result of the gravity is relatively small in most thermodynamic systems and is usually disregarded. If a system involves two phases, it will be in phase equilibrium only when the mass of each phase reaches an equilibrium level and stays there. A system will be in chemical equilibrium if its chemical composition does not change with time, that is, no net chemical reaction occurs within the system. A system will be in thermodynamic equilibrium only when it satisfies the conditions for all modes of equilibrium. 1.7 Thermal and Calorical Properties The equation pv = RT or p/ρ = RT is called thermal equation of state , where p , T and v (= 1 /ρ ) are thermal properties and R is the gas constant. A gas which obeys the thermal equation of state is called thermally perfect gas . Any relation between the calorical properties, u , h and s and any two thermal properties is called calorical equation of state . In general, the ther-modynamic properties (the properties which do not depend on process) can 16 Basic Concepts and Definitions be grouped into thermal properties ( p , T , v ) and calorical properties ( u , h , s ). Two calorical state equations which are extensively used are the following [1]. u = u ( T, v ) , h = h ( T, p ) where u is the specific internal energy and h is the specific enthalpy, which is a combination property, defined as the sum of internal energy and flow work ( pv ).
eBook - PDFStatistical and Thermal Physics
Fundamentals and Applications
- M.D. Sturge(Author)
- 2018(Publication Date)
- A K Peters/CRC Press(Publisher)
Chapter 2 Temperature, Work, and Heat We de h ne thermodynamics. . . as the investigation of the dynamical and thermal properties of bodies, deduced entirely from the h rst and second laws of thermodynamics, without speculation as to the mole-cular constitution. –J. Clerk Maxwell Classical thermodynamics. . . is the only physical theory of universal content which I am convinced. . . will never be overthrown. –Albert Einstein 2.1 Thermal Equilibrium and the Zero’th Law of Thermodynamics Thermal physics can be de h ned as the study of all physical processes in-volving temperature or heat. However, the precise meaning of these two words needs to be examined carefully. We start with temperature. We all have an intuitive sense of temperature (“Phew, it’s hot in here”), but this sense is of very little use in physics because it is so subjective (“You think so? I h nd it rather chilly”). 1 To get a more objective view we use a thermometer, but what does it actually measure? What do we mean when we interpret the length of a column of mercury as a measure of temperature? Before we can answer these questions, we need to introduce the concepts of Thermal Equilibrium and of insulating (or isolating) and diathermal walls. 1 If you are in any doubt about the subjectivity of one’s sense of temperature, try the following experiment. Take three bowls of water, one as hot as you can stand, one ice-cold, and one tepid. Put your right hand in the hot water and your left in the cold for about a minute. Then put both hands in the tepid water. Your right hand will tell you that this water is cool, your left that it is warm. 5 6 2. Temperature, Work, and Heat If we dip a mercury thermometer into co ee straight from the co ee machine, we see that the length of the mercury column changes initially, but soon settles down at a new steady value, the “reading”. The thermometer is now said to be in Thermal Equilibrium (which we will often shorten to “equilibrium”) with the co ee.
eBook - PDF- Shang???Keng Ma(Author)
- 1985(Publication Date)
- WSPC(Publisher)
PARTI EQUILIBRIUM This part is divided into four chapters which introduces the basic concepts of equilibrium and provides some simple examples. The first two chapters review the concept of equilibrium and the laws of thermodynamics, with special emphasis on the facts that equilibrium is not an instantaneous state and the observation time is important. The outstanding feature of thermodynamics is the appearance of entropy. Chapter 3 discusses the law of detailed balance, pointing out the interaction between molecules as the origin of equilibrium. Chapter 4 discusses electrons in metals, reviewing some basic knowledge in solid state physics and some elementary calculations in statistical mechanics. This part lays the preparatory ground work. Various basic concepts will be analysed again in the following parts. Chapter 1 EQUILIBRIUM This chapter discusses the fundamental concept of equilibrium with emphasis on the relation between equilibrium and the observation time. On the time scale of molecular motion, equilibrium is a state characterizing the system over a long observation time and not an instantaneous state. To discuss equilibrium we must consider the approximate length of the observation time. 1.1. Equilibrium and Observation Time Basic concepts always originate from simple phenomena. Equilibrium is the most basic concept of thermodynamics and statistical mechanics. We use a few simple examples to illustrate the meaning of equilibrium and to discuss some of its related problems. Equilibrium refers to a state which is unchanging. For example, an ancient painting hanging on the wall is an unchanging state. However, to say this state is unchanging is only an approximation and is not absolute. From the date of its creation to the present, this ancient painting has undergone many changes. For example, because of the chemical reaction with air, some pigments have changed and the paper has become pale.
No longer available |Learn more- Irving Granet, Maurice Bluestein(Authors)
- 2014(Publication Date)
- CRC Press(Publisher)
The first is an interchange of energy, and the second is that this interchange would not have taken place if there were no temperature difference between the system and its surroundings. Therefore, we may define heat as the energy in transition across the boundaries of a system due to a temperature difference between the system and its surroundings. In this defini-tion of heat, the transfer of mass across the boundaries of the system is excluded. It should be noted that this indicates a similarity between heat and work. Both are energies in tran-sition, and neither is a property of the system in question. Just as in work, heat can transfer quasi-statically to or from a system. The difference in temperature between the system and its surroundings for quasi-static heat transfer can be only an infinitesimal amount at any time. Once again, it is necessary to adopt a convention for the energy interchanged by a system with its surroundings. We shall use the convention that heat to a system from its surroundings is positive and that heat out of a system is negative . To learn these conventions, it is convenient to consider the typical situation in which heat is transferred to a system to obtain useful work from the system. This sets the convention that heat into a system is positive and work out of the system is also positive. Positive in this sense means either desirable or conventional from the viewpoint of conventional power cycles. For refrigera-tion cycles, the opposite of this convention will be more useful. It is important to recognize the difference between heat and temperature. Temperature is a measure of the energy contained in the molecules of a system due to their motion. When the temperature of a system is greater than that of its surroundings, some of that molecular energy is transferred to the surroundings in what we call heat. Thus, tempera-ture is a property of a system in a given state, whereas heat is associated with a change in the state of a system.
- Andrei D. Polyanin, Alexei Chernoutsan(Authors)
- 2010(Publication Date)
- CRC Press(Publisher)
This equation relates three coefficients α = 1 V parenleftBig ∂V ∂T parenrightBig p ( thermal volume expansion coefficient ), β = 1 p parenleftBig ∂p ∂T parenrightBig V ( thermal pressure coefficient ), K = – V parenleftBig ∂p ∂V parenrightBig T ( isothermal bulk modulus ). ◮ Nonequilibrium systems. Equilibrium thermodynamics deals with equilibrium states and processes. It can judge the direction of nonequilibrium processes between the ini-tial and final equilibrium states but cannot provide quantitative characterization of these processes. Nonequilibrium systems are studied by physical kinetics and nonequilibrium thermodynamics . Note that the time in which a system comes to equilibrium ( relaxation time ) decreases with decreasing system size, and therefore the term local equilibrium in a small portion of a nonequilibrium system makes sense. Consequently, it is meaningful to speak of local thermodynamic parameters (functions of state) that vary from point to point in a nonequilibrium system (e.g., temperature T ( r )). An important role in studying nonequilibrium systems is played by the notions of flux of a physical quantity (e.g., the number of molecules, mass, momentum, energy, charge, etc.) through a given surface and flux density at a given point in space. P2.2. F IRST L AW OF T HERMODYNAMICS 443 For instance, energy flux W equals the amount of energy transferred through a surface per unit time (measured in J/s, or W). A flux density is a vector quantity that characterizes the direction and intensity of transfer of a physical quantity through a given point in space. For instance, energy flux density w equals in magnitude to the ratio of the energy flux Δ W through a small surface to the area Δ S of this surface (measured in W / m 2 ) in the limit Δ S → 0 . Among all small surfaces through the given point, one must take one for which the above ratio is maximum.
eBook - PDF- R. Prasad(Author)
- 2016(Publication Date)
- Cambridge University Press(Publisher)
This is the basis of carbon dating technique used to determine the age of biological samples. It may again be observed that the steady state in the relative concentrations of the stable and the radioactive carbon isotopes in living organism is maintained by the energy that living organism get from their food. Summing up it may be said that the maintenance of steady state requires a continuous source of energy, while the maintenance of equilibrium does not need any source. If a system in steady state is left to itself after removing the source of energy, after some time eventually the system will again attain equilibrium. But this time the system will attain natural equilibrium. Steady state basically represents a group the natural equilibrium is a subset of this group. Apart from Thermal Equilibrium, which establishes the equality of temperature, there may be other types of equilibriums also. Examples are mechanical equilibrium and chemical equilibrium. Thermal Equilibrium is characterized by the equality of temperature, mechanical equilibrium by the minimum of the potential energy and the chemical equilibrium by the law of mass action. A system is said to be in thermodynamic equilibrium when it is simultaneously in thermal, mechanical and chemical equilibrium. As will be seen later some thermodynamical functions play the same role in determining the stability of systems as is played by potential energy in determining the stability of mechanical systems. 3.5 Processes In section 3.2 it was shown that a system in equilibrium may be represented by a point in the N- dimensional space made up of N-system variables. In order to change the state of a system, say from state A to state B, (see Fig. 3.2) some operations have to be performed. The operations that change the state of the system are called processes and are represented by lines/ curves on the N-dimensional space made of state variables. These curves/lines join the initial and the final states of the system.
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