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Physics LibreTexts

1.2: The Zeroth Law of Thermodynamics

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This can be stated as follows.

Zeroth Law of Thermodynamics:

If two bodies A and B are in thermal equilibrium with a third body C, then they are in thermal equilibrium with each other.

Consequences of the Zeroth Law

Thermal equilibrium of two bodies will mean a restrictive relation between the thermodynamic coordinates of the first body and those of the second body. In other words, thermal equilibrium means that

F(xA,xB)=0

if A and B are in thermal equilibrium. Thus the zeroth law states that

F(xA,xB)=0F(xB,xC)=0}F(xA,xC)=0

This is possible if and only if the relations are of the form

F(xA,xB)=t(xA)t(xB)=0

This means that, for any body, there exists a function t(x) of the thermodynamic coordinates x, such that equality of t for two bodies implies that the bodies are in thermal equilibrium. The function t is not uniquely defined. Any single-valued function of t, say, T(t) will also satisfy the conditions for equilibrium, since

tA=tBTA=TB

The function t(x) is called the empirical temperature. This is the temperature measured by gas thermometers.

The zeroth law defines the notion of temperature. Once it is defined, we can choose n+1 variables (x,t) as the thermodynamic coordinates of the body, of which only n are independent. The relation t(x) is an equation of state.


This page titled 1.2: The Zeroth Law of Thermodynamics is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by V. Parameswaran Nair via source content that was edited to the style and standards of the LibreTexts platform.

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