Question about the 0th law of thermodynamics

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SUMMARY

The discussion centers on the 0th law of thermodynamics, specifically the equilibrium relationships among three systems: A, B, and C. It establishes that if systems A and B are in equilibrium with system C at the same thermodynamic coordinates, they must also be in equilibrium with each other. The participant questions the implications of varying pressure (P) and volume (V) combinations that yield the same product (PV), suggesting that this merely indicates identical temperatures rather than true equilibrium. A reference to Kenneth Denbigh's "The Principles of Chemical Equilibrium" is provided for further clarification.

PREREQUISITES
  • Understanding of thermodynamic laws, particularly the 0th law of thermodynamics.
  • Familiarity with the concepts of pressure (P), volume (V), and temperature (T) in thermodynamic systems.
  • Knowledge of equilibrium conditions in chemical systems.
  • Ability to interpret mathematical relationships in thermodynamics.
NEXT STEPS
  • Study the implications of the 0th law of thermodynamics in various systems.
  • Explore the mathematical relationships between pressure, volume, and temperature in non-ideal gases.
  • Read Kenneth Denbigh's "The Principles of Chemical Equilibrium" for deeper insights into equilibrium concepts.
  • Investigate the conditions under which different thermodynamic systems can be considered in equilibrium.
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Students of thermodynamics, physicists, chemists, and anyone interested in the foundational principles of thermal equilibrium and system interactions.

QuasarBoy543298
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assume I have 3 systems a,b and c.
the equilibrium between a and c can be described by the equality PcVc = f(A1,..., An)
and the same for b and c - PcVc = g(B1,...,Bk).
why does the equality g(B1,..., Bk) = f(A1,..., An) describes an equilibrium between A and B?
the 0th law states that if A and B are in equilibrium with c **for the same value of the thermodynamics coordinates of C**
then they are in equilibrium with each other, but I can find different pairs of Pc and Vc that will result in the same value of PcVc.
 
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Isn’t PV proportional to T? So this just describes three systems with the same temperature.
 
I'm not talking about ideal gas but on general systems.
you can take another combination as well, such as PN, and the question stays the same.
 
A persuasive representation which – to my mind – addresses your question can be found in “The Principles of Chemical Equilibrium“ (see pages 9-13) by Kenneth Denbigh.
https://archive.org/details/ThePrinciplesOfChemicalEquilibrium/page/n30
 

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