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The zeroth law of thermodynamics may be succintly stated as: The laws of Thermodynamics in principle describe the specifics for the transport of heat and work in thermodynamic processes. ...
Conservation of energy (the first law of thermodynamics) is one of several conservation laws. ...
The most concise statement of the second law of thermodynamics states that the total entropy of any isolated thermodynamic system tends to increase over time, approaching a maximum value. ...
The third law of thermodynamics was developed by Walther Nernst and is thus sometimes referred to as Nernsts theorem. ...
Thermodynamics (from the Greek thermos meaning heat and dynamis meaning power) is a branch of physics that studies the effects of temperature on physical systems at the macroscopic scale. ...
- If two thermodynamic systems A and B are in thermal equilibrium, and B and C are also in thermal equilibrium, then A and C are in thermal equilibrium.
A system in thermal equilibrium is a system whose properties (like pressure, temperature, volume, etc.) are not changing in time. A hot cup of coffee in your kitchen is not at equilibrium with its surroundings, because it is cooling down, its temperature is dropping. Once its temperature stops decreasing, it will be at room temperature, and it will be in thermal equilibrium with its surroundings. In thermodynamics, a thermodynamic system is in thermal equilibrium or thermodynamic equilibrium when its macroscopic observables have ceased to change with time -- for example, an ideal gas whose distribution function has stabilised to a Maxwell-Boltzmann distribution. ...
Two systems are in thermal equilibrium with each other if they are in thermal contact with each other and neither system is changing in time. Thermal contact means they are able to transfer heat to each other: If one is hot and the other cold, the the hot one will warm the cold one and vice versa. More generally, two systems can be in thermal equilibrium without thermal contact if one can be certain that if they were thermally connected, their properties would not change in time.
Mathematically, the zeroth law expresses the transitivity of the equilibrium relationship. Two other trivial properties of the equilibrium relationship are often included in the statement of the third law: In mathematics, a binary relation R over a set X is transitive if it holds for all a, b, and c in X, that if a is related to b and b is related to c, then a is related to c. ...
- reflexivity - a system in thermal equilibrium is in thermal equilibrium with itself.
- symmetry - if system A is in thermal equilibrium with system B, then system B is in thermal equilibrium with system A.
These are included because, together with the transitivity statement, the equilibrium relationship between two systems becomes what mathematicians call an equivalence relation which allows a number of mathematical theorems to be easily proven. Also, we will not need to make statements like "if A and B are in equilibrium with C then they are in equilibrium with each other" which does not follow from transitivity alone, but does follow from transitivity and symmetry. In mathematics, an equivalence relation on a set X is a binary relation on X that is reflexive, symmetric and transitive, i. ...
Description Two systems are said to be in thermal equilibrium when 1) both of the systems are in a state of equilibrium, and 2) they remain so when they are brought into contact, where 'contact' is meant to imply the possibility of exchanging heat, but not work or particles. Thus, thermal equilibrium is a relation between thermodynamical systems. In the following we will write  for 'A is in thermal equilibrium with B'.
The zeroth law states that this relation is transitive, which means that whenever system A is in thermal equilibrium with B, and B is in thermal equilibrium with system C, then A and C are also in thermal equilibrium. Formally: In mathematics, a binary relation R over a set X is transitive if it holds for all a, b, and c in X, that if a is related to b and b is related to c, then a is related to c. ...
The zeroth law: 
 A,B,C system at thermal equilibrium Image File history File links Download high resolution version (1240x551, 51 KB) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...
Image File history File links Download high resolution version (1240x551, 51 KB) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...
Temperature and the zeroth law It is often claimed, for instance by Max Planck in his influential textbook on thermodynamics, that this law proves that we can define a temperature function, or more informally, that we can 'construct a thermometer'. Whether this is true is a subject in the philosophy of thermal and statistical physics. We will look at it in a formal way. Max Planck This article is about Planck, the German physicist. ...
A thermometer is a device used to measure temperatures or temperature changes. ...
The philosophy of thermal and statistical physics is one of the major subdisciplines of the philosophy of physics. ...
Definition: If we can assign to the state spaces of all thermodynamical systems  functions  such that  , where sX is the state of system X, we can define a temperature function. In computer science, a state space is a description of a configuration of states used as a simple model of machines. ...
Claim: The zeroth law of thermodynamics implies that we can define a temperature function.
It is easy to see that the zeroth law is a necessary condition for the existence of a temperature function. The '=' in ΘA(sA) = ΘB(sB) is, of course, a transitive relation, so  should be so as well. The '=' relation is not just transitive, it is an equivalence relation, which means that it is reflexive, symmetric and transitive. We would need two additional 'laws of thermodynamics' to express this: In mathematics, an equivalence relation on a set X is a binary relation on X that is reflexive, symmetric and transitive, i. ...
Reflexivity: 
Symmetry: 
The relation "is in equilibrium with" is symmetric by definition. It is trivial to extend the relation "is in equilibrium with" so that A~A.
The temperature so defined may indeed not look like the Celsius temperature scale, or even be continuous, but it is a temperature function.
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 parameter P, V and n, they are 2D surfaces).
For example, if two systems of ideal gas are in equilibrium, then P1V1/N1 = P2V2/N2 where Pi is the pressure in the ith system, Vi is the volume, and Ni is the 'amount' (in moles, or simply number of atoms) of gas. Mole may mean: Mole (animal), a small burrowing mammal Mole (espionage), a spy working under deep cover Mole (sauce), a Mexican sauce made from chile peppers and other spices, including chocolate Mole (skin marking), a small spot of darkened pigment on the skin Mole (unit) is the SI unit for...
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.
Time and the zeroth law While the zeroth law specifies the condition of thermal reflexivity and thermal symmetry, it does not specify the time required in order to meet such a condition. For example if system A is at 30 degrees, system B is at 50 degrees, and system C is at 20 degrees, a certain amout of time is required before thermal reflexivity and symmetry are achieved. The proposition that time is required to achieve thermal equilibrium is a necessary consequence of the second law of thermodynamics - regarding an increase in entropy - when the A,B,C system is at disequilibrium. The most concise statement of the second law of thermodynamics states that the total entropy of any isolated thermodynamic system tends to increase over time, approaching a maximum value. ...
 A,B,C system at disequilibrium Image File history File links Download high resolution version (1240x551, 51 KB) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...
Image File history File links Download high resolution version (1240x551, 51 KB) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...
The name The term zeroth law was coined by Ralph H. Fowler. In many ways, the law is more fundamental than any of the others. However, the need to state it explicitly as a law was not perceived until the first third of the 20th century, long after the first three laws were already widely in use and named as such, hence the zero numbering. There is still some discussion about its status in relation to the other three laws. The zeroth item is the initial item of a sequence, if that sequence is numbered beginning from zero rather than one. ...
Ralph Howard Fowler (January 17, 1889 – July 28, 1944) was a British physicist and astronomer. ...
(19th century - 20th century - 21st century - more centuries) Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s As a means of recording the passage of time, the 20th century was that century which lasted from 1901–2000 in the sense of the Gregorian calendar (1900–1999 in the...
Zero can refer to several things. ...
References - Jos Uffink, J. van Dis, S. Muijs; Grondslagen van de Thermische en Statistische Fysica; Utrecht University
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