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The zeroth law of thermodynamics may be succinctly stated as:
Description
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 off and decreasing in temperature. Once its temperature stops decreasing, it will be at room temperature, and it will be in thermal equilibrium with its surroundings.
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. And 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.
Thus, thermal equilibrium is a relation between thermodynamical systems. Mathematically, the zeroth law expresses that this relation is an equivalence relation. (Technically, we would need to also include the condition that a system is in thermal equilibrium with itself.)
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.
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). The temperature so defined may indeed not look like the Celsius temperature scale, but it is a temperature function.
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.
The surface defines surfaces of equal temperature, and the obvious (but not only) way to label them is to define T so that where R is some constant. These systems can now be used as a thermometer to calibrate other systems.
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.
References
- Jos Uffink, J. van Dis, S. Muijs; Grondslagen van de Thermische en Statistische Fysica; Utrecht University
External links
Нулев закон на термодинамиката | Nultý termodynamický zákon | Termodynamikkens 0. lov | Thermodynamik#Nullter Hauptsatz (manchmal auch 4. Hauptsatz genannt) | Principio Cero de la Termodinámica | قانون صفرم ترمودینامیک | Principe zéro de la thermodynamique | Lei Cero da Termodinámica | Principio zero della termodinamica | Nulde wet van de thermodynamica | Zerowa zasada termodynamiki | Lei zero da termodinâmica | Нулевое начало термодинамики | Nultý termodynamický zákon | Termodynamikens nollte huvudsats | กฎข้อที่ศูนย์ของอุณหพลศาสตร์ | 热力学第零定律
"Zeroth law of thermodynamics"