Need help understanding this thermo. derivation

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Discussion Overview

The discussion centers around understanding the derivation of the expression for (\frac{\partial T}{\partial P})_s in terms of temperature (T), specific volume (V), heat capacity at constant pressure (C_p), thermal expansion coefficient (\alpha), and isothermal compressibility (\kappa_T). The context involves thermodynamics, specifically focusing on reversible adiabatic processes.

Discussion Character

  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant seeks clarification on deriving (\frac{\partial T}{\partial P})_s and expresses difficulty following the book's derivation.
  • Another participant notes the complexity of the derivation and asks where the original poster is lost.
  • A third participant offers an alternative derivation using ordinary partial derivative notation, indicating confusion with the original notation.
  • A later reply expresses gratitude for the alternative derivation, confirming that it alleviates some confusion regarding the notation used in the book.

Areas of Agreement / Disagreement

The discussion reflects a lack of consensus on the clarity of the original derivation, with participants expressing varying levels of understanding and confusion regarding the notation and steps involved.

Contextual Notes

Participants have not settled on specific assumptions or definitions related to the notation used in the derivation, which may contribute to the confusion experienced.

mdawg467
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Im trying to understand this concept of deriving an expression for (\frac{\partial T}{\partial P})s in terms of T, V, Cp, \alpha, and \kappaT

(\frac{\partial T}{\partial P})s is evaluated by measuring the temperature change and the specific volume change accompanying a small pressure change in a reversible adiabatic process.

I attached the derivation that the book does, but I cannot follow it. Any help would be greatly appreciated!

Thanks
 

Attachments

  • 20130406_173018-1.jpg
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There are a lot of steps in that simple looking derivation. Where are you lost?
 
Don't understand the notation in your thumbnail, but append my derivation, expressed in ordinary partial derivative notation.
 

Attachments

  • Thermod formula.jpg
    Thermod formula.jpg
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Philip Wood said:
Don't understand the notation in your thumbnail, but append my derivation, expressed in ordinary partial derivative notation.

Thanks dude, I was getting lost with the notation as well. This helps out big time.. Not sure what the book was doing lol.
 

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