Equation of State: Internal Interventions

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Discussion Overview

The discussion revolves around the concept of an equation of state, particularly exploring the implications of including internal energy (U) in the formulation. Participants consider whether a modified equation involving internal energy can still be classified as an equation of state, and the relationship between various thermodynamic variables.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant suggests that the equation U=cte*PV could be considered an equation of state, questioning the role of internal energy in this context.
  • Another participant raises concerns about how to determine the values of U or the constant (cte), indicating a need for clarity on these variables.
  • A clarification is provided that U represents internal energy and cte is a constant, with a specific example given as cte=3/2.
  • It is noted that an equation of state relates state variables, and the proposed equation could be seen as a trivial modification of existing equations due to a linear relationship between U and temperature (T).
  • Further elaboration suggests that if U is expressed in terms of extensive parameters like entropy (S), volume (V), and number of moles (n), it could lead to a fundamental equation from which multiple equations of state could be derived.

Areas of Agreement / Disagreement

Participants express differing views on the classification of the proposed equation involving internal energy, with some supporting its validity as an equation of state while others highlight the need for further specification of variables. The discussion remains unresolved regarding the implications of including internal energy in the equation of state.

Contextual Notes

There are limitations regarding the definitions of the variables involved, particularly the constant (cte) and its relation to internal energy. The discussion also reflects uncertainty about the conditions under which the proposed equation holds true.

M. next
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It is known that the combination of (p, v, t) gives Equation if State. Okay, what if we have the intervention of the internal as well, i.e, U=cte*PV for example. Can this be also considered as an equation of state?
 
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How do we know what U or cte are?
 
Excuse me, U: internal energy. Cte any constant relating those variables. My case was cte=3/2
 
An equations of state is an equation that relates state variables, so yes, that would be an equation of state. Note that your example is just a trivial modification of the usual equation of state, due to the fact that there is a direct linear relation between U and T.
 
M. next said:
It is known that the combination of (p, v, t) gives Equation if State. Okay, what if we have the intervention of the internal as well, i.e, U=cte*PV for example. Can this be also considered as an equation of state?

If you give such a U (notice that it depends explicitly on some intensive parameters), it would be an equation of state. If you however give U in function of S, V and n (extensive parameters), you have all the information of the system and in such a case you'd have a fundamental equation from which you could derive up 3 equations of state.
 
Thank you both for clearing things up!
 

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