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zeroth law of thermodynamics

 Definition/Summary If body A is in thermal equilibrium with body B, and body C is in thermal equilibrium with body B, then body A is in thermal equilibrium with body C. The concept which arises from the zeroth law is that of temperature.

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 Breakdown Physics > Statistical & Thermal >> Thermodynamic Laws

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 Extended explanation Formal Argument in Favour of Temperature Consider three systems of gas A, B and C. If A and B are in thermal equilibrium then there is a definite relationship between PA VA & PB VB. We can write this relationship as: $$F_1 (P_A,V_A,P_B,V_B) = 0$$ Likewise for gases B and C: $$F_2 (P_B, V_B,P_C,V_C) = 0$$ Rearranging the equations above: $$P_B = f_1(P_A,V_A,V_B) = f_2(P_C,V_C,V_B)$$ From the zeroth law we have: $$F_3(P_A, V_A,P_C,V_C) = 0$$ So: $$P_A=f_3(V_A,P_C,V_C)$$ Thus VB does not need to appear and can be removed from previous functions. So for systems in thermal equilibrium, there is a function of their parameters that is common to both systems. i.e. $$f(P,V) = \theta$$ where $\theta$ is empirical temperature and $f(P,V)$ is the equation of state. So we can say that two objects in thermal equilibrium have the same temperature.

Commentary

 Kurdt @ 06:26 AM Jun16-08 It is conveying the important concept of temperature. It is basically stating that if there is no heat energy transfer between two bodies in thermal contact, then they are both at the same temperature.

 MariusP @ 02:25 PM Jun11-08 well, it is correct , but can this be called a physical law? I think it is simple mathematical implication. If A=B and B=C than A=C.... it is a valid statement for all cases in which this relation appears.

 Kurdt @ 08:42 AM May13-08 Images should be showing now. I think the definition is fine as it is. There are many different ways of saying the same thing.

 Accio @ 06:33 AM May13-08 Images of equations are not shown!

 Carcul @ 03:34 AM May13-08 The statement of the zeroth law I teach my students is the following (very similar): "If body A is in thermal equilibrium with body B, and body C is in thermal equilibrium with body B, then body A is in thermal equilibrium with body C, and, by definition of temperature, the three bodies are at the same temperature."