Thermodynamics for radiating shells in anti-de Sitter space-time

Zeroth Law of ThermodynamicsIn physics and physical chemistry, the zeroth law of thermodynamics is a generalization about the thermal equilibrium between bodies, or thermodynamic systems, in contact. It results from the definition and properties of temperature.Zeroth law as equivalence relationA system is said to be in thermal equilibrium when its temperature does not change over time. Let A, B, and C be distinct thermodynamic systems or bodies. The zeroth law of thermodynamics can then be expressed as:"If A and B are each in thermal equilibrium with C, A is also in thermalequilibrium with B."The preceding sentence asserts that thermal equilibrium is a Euclidean relation betweenthermodynamic systems. If we also grant that all thermodynamic systems are (trivially) in thermal equilibrium with themselves, then thermal equilibrium is also a reflexive relation. Relations that are both reflexive and Euclidean are equivalence relations. One consequence of this reasoning is that thermal equilibrium is a transitive relation between the temperature T of A, B, and C:if T (A) = T (B)if T (B) = T (C)then T (A) = T (C)Thermal equilibrium between many systemsMany systems are said to be in equilibrium if the small exchanges (due to Brownian motion, for example) between them do not lead to a net change in the total energy summed over all systems.A simple example illustrates why the zeroth law is necessary to complete the equilibrium description.Consider N systems in adiabatic isolation from the rest of the universe (i.e no heat exchange is possible outside of these N systems), all of which have a constant volume and composition, and which can only exchange heat with one another.The combined First and Second Laws relate the fluctuations in total energy, δU , to the temperature of the i th system, T i and the entropy fluctuation in the i th system, δS i as follows:∑=Ni i i S T U δδThe adiabatic isolation of the system from the remaining universe requires that the total sum of the entropy fluctuations vanishes, or:0δ=∑N i i SThat is, entropy can only be exchanged between the N systems. This constraint can be used to rearrange the expression for the total energy fluctuation and obtain:()∑−=Ni i j i S T T U δδwhere T j is the temperature of any system j we may choose to single out among the N systems. Finally, equilibrium requires the total fluctuation in energy to vanish, in which case:()0δ=−∑N i i j i S T Twhich can be thought of as the vanishing of the product of an antisymmetric matrix T i - T j and a vector of entropy fluctuations δS i . In order for a non-trivial solution to exist,δS i≠ 0That is, the determinant of the matrix formed by T i - T j must vanish for all choices of N. However, according to Jacobi's four-square theorem, the determinant of a NxN antisymmetric matrix is always zero if N is odd, although for N even we find that all of the entries must vanish, T i - T j = 0 , in order to obtain a vanishing determinant. Hence T i = T j at equilibrium. This non-intuitive result means that an odd number of systems are always in equilibrium regardless of their temperatures and entropy fluctuations, while equality of temperatures is only required between an even number of systems to achieve equilibrium in the presence of entropy fluctuations.The zeroth law solves this odd vs. even paradox, because it can readily be used to reduce anodd-numbered system to an even number by considering any three of the N systems and eliminating one by application of its principle, and hence reduce the problem to even N which subsequently leads to the same equilibrium condition that we expect in every case, i.e., T i = T j . The same result applies to fluctuations in any extensive quantity, such as volume (yielding the equal pressure condition), or fluctuations in mass (leading to equality of chemical potentials). Hence the zeroth law has implications for a great deal more than temperature alone. In general, we see that the zeroth law breaks a certain kind of asymmetry present in the First and Second Laws. Temperature and the zeroth lawIt is often claimed, for instance by Max Planck in his influential textbook on thermodynamics, that the Zeroth law implies that we can define a "temperature function" or more informally, that we can "construct a thermometer." Just what this means is a topic in the philosophy of thermal and statistical physics.In the space of thermodynamic parameters, zones of constant temperature will form a surface, which provides a natural order of nearby surfaces. It is then simple to construct a global temperature function that provides a continuous ordering of states. Note that the dimensionality of a surface of constant temperature is one less than the number of thermodynamic parameters (thus, for an ideal gas described with 3 thermodynamic parameters p, V and n, it is a 2 dimensional surface). The temperature so defined may indeed not look like the Celsius temperature scale, but it is a temperature function nonetheless.For example, if two systems of ideal gas are in equilibrium, then p1V1/n1 = p2V2/n2 where p i is the pressure in the i th system, V i is the volume, and n i is the "amount" (in moles, or simply the number of atoms) of gas.The surface pV/n = const defines surfaces of equal temperature, and the obvious (but not only) way to label them is to define T so that pV/n = RT, where R is some constant. These systems can now be used as a thermometer to calibrate other systems.HistoryThe term zeroth law was coined by Ralph H. Fowler in the 1920s. This law is arguably the most fundamental of the four numbered laws of thermodynamics. It was called the zeroth law because the need to state it explicitly was not understood until after the First, Second, and Third Laws had been named and become commonplace.The zeroth lawThe zeroth law is a consequence of thermal equilibrium and allows us to conclude that temperature is a well-defined physical quantity. The zeroth law of thermodynamics states:If a body A and a body B are both in equilibrium with each other; then a body C which is in thermal equilibrium with body B will also be in equilibrium with body Aand the temperature of body C is equal to the temperature of body A.It is the zeroth law, because it preceeds the first and second laws of thermodynamics and is also a tacit assumption in both laws.We use the zeroth law when we wish to compare the temperatures of two objects, A and B. We can do this by using a thermometer, C and placing it again object A it reaches thermal equilibrium with object A and measure the temperature of A. Placing the thermometer against object B until thermal equilibrium is reached we measure the temperature of object B. If they are the same temperature then they will be in thermal equilibrium with each other.Figure 1. The Zeroth law of thermodynamics.。

热力学专业英语作文Title: Thermodynamics in EnglishThermodynamics is the branch of physics that deals with the relationships between heat, work, energy, and temperature.It is one of the fundamental sciences that help us understand and predict the behavior of systems.In this essay, we will explore some key concepts and terms related to thermodynamics in English.Firstly, let"s talk about the laws of thermodynamics.There are four laws of thermodynamics, but the first and second laws are the most fundamental.The first law of thermodynamics, also known as the law of conservation of energy, states that energy cannot be created or destroyed, only transformed from one form to another.The second law of thermodynamics states that in a closed system, the total entropy always tends to increase over time, meaning that processes tend to become more disordered.ext, let"s discuss some common units of measurement in thermodynamics.The joule (J) is the unit of energy in the International System of Units (SI), while the calorie (cal) is a non-SI unit of energy commonly used in nutrition.The watt (W) is the unit of power, which is the rate at which work is done or energy is transferred.The kilowatt-hour (kWh) is a common unit of energy consumption, often used in the context of electricity usage.Thermodynamic properties are characteristics of a system that can be used to describe its state and predict its behavior.Some common thermodynamic properties include temperature, pressure, volume, and internal energy.Temperature is a measure of the average kinetic energy of the particles in a system, while pressure is a measure of the force exerted by the particles on the walls of the container.Volume is the amount of space occupied by the system, and internal energy is the total energy of the system, including both kinetic and potential energy.ow, let"s talk about some thermodynamic processes.An isothermal process is a process in which the temperature of the system remains constant.A reversible process is one that can be undone by a small change in the system"s state, while an irreversible process is not reversible and may involve a large change in the system"s state.An adiabatic process is one in which there is no heat transfer between the system and its surroundings, while a diabatic process involves heat transfer.In conclusion, thermodynamics is a fundamental science that helps us understand the behavior of systems.By studying the laws of thermodynamics, units of measurement, thermodynamic properties, and processes, we can gain a deeper understanding of how energy and heat are transformed and transferred.With this knowledge, we can apply thermodynamics to various fields, such as engineering, physics, andchemistry, to solve real-world problems and improve our lives.。