Equation of State: Internal Interventions

AI Thread Summary
The discussion explores the concept of an equation of state, particularly in relation to internal energy (U) and its dependence on pressure (P), volume (V), and temperature (T). It is established that a modified equation, such as U = cte * PV, can still qualify as an equation of state if it relates state variables. The conversation highlights that if U is expressed in terms of extensive parameters like entropy (S), volume (V), and number of particles (n), it provides comprehensive information about the system, allowing derivation of multiple equations of state. The relationship between U and T is noted as a direct linear connection. Overall, the discussion clarifies how internal energy can be integrated into the framework of equations of state.
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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