Equations of state = superfluous state variables?

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SUMMARY

This discussion centers on the necessity of equations of state in thermodynamics, particularly questioning their relevance when sufficient state variables like pressure (P) and volume (V) are available. The argument posits that equations of state may be redundant if one can adequately describe a system using fewer variables. However, it highlights scenarios where measuring P and V is impractical, such as when only temperature is known, emphasizing the importance of equations of state for comprehensive analysis, especially during phase transitions at constant temperature.

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AcidRainLiTE
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I don't get the point of equations of state since they seem to me to just indicate that we defined too many state variables. Why not just trim down our set of state variables and do away with the equations of state (i.e. for an ideal gas, just notice that P and V are sufficient to describe the system)?
 
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But what if you can't measure P and V? What if you know the volume of a vessel and you have a thermometer, but no manometer. How are you to work with that if you don't have an equation of state?

And what about processes that take place at constant T, like phase changes? Do you really want to describe the liquid -> gas transition only in terms of P and V?
 

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