Which should I use to prove this?

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Discussion Overview

The discussion revolves around the selection of appropriate thermodynamic equations and relationships, particularly in the context of deriving expressions involving entropy (s), internal energy (u), and enthalpy (h) at constant volume. Participants explore various equations and their implications in gas theory.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents the equation (∂s/∂P) at constant volume = 1/T × (∂u/∂T) at constant volume × (∂T/∂P) at constant volume and asks for guidance on which formula to use.
  • Another participant notes that among the provided formulas, only Tds = du + pdv is a valid equation and questions how to express it under constant volume conditions.
  • A different participant suggests that the other variables can also be expressed as functions of volume and pressure, leading to the formulation of ∂s = (∂s/∂p)dp + (∂s/∂v)dv.
  • One participant proposes using Maxwell relations to aid in the derivation but notes a lack of understanding regarding them.
  • Another participant expresses that they derived (∂s/∂P) at constant volume = (1/T)(∂h/∂P) at constant volume - (v/T) and requests others to share their workings.

Areas of Agreement / Disagreement

Participants express differing levels of understanding regarding the equations and concepts involved, with some suggesting specific approaches while others seek clarification. No consensus is reached on the best method or formula to use.

Contextual Notes

There are limitations in the discussion regarding the understanding of Maxwell relations and the application of the equations under constant volume conditions. Some participants express uncertainty about the derivations and implications of the equations presented.

Outrageous
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(∂s/∂P) at constant volume =1/T ×(∂u/∂T)at constant volume × (∂T/∂P) at constant volume

s(P,v)
Tds= du +pdv
h= u + pv
h(P,v)
u(P,v)
or other formula?
How am I going to choose ? Please guide

Thank
 
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Outrageous said:
(∂s/∂P) at constant volume =1/T ×(∂u/∂T)at constant volume × (∂T/∂P) at constant volume

s(P,v)
Tds= du +pdv
h= u + pv
h(P,v)
u(P,v)
or other formula?
I'm not expert on gas theory, so I'll just treat this as an algebraic question.
Of those 'formulae', only two are equations. One of those two involves h, not mentioned anywhere else. So that leaves Tds= du +pdv as the only candidate.
What would the constant volume version of that equation look like?
 
haruspex said:
I'm not expert on gas theory, so I'll just treat this as an algebraic question.
Of those 'formulae', only two are equations. One of those two involves h, not mentioned anywhere else. So that leaves Tds= du +pdv as the only candidate.
What would the constant volume version of that equation look like?

The others also can become equation like s is function of v and p
So ∂s=(∂s/∂p)dp + (∂s/∂v)dv
Then h=u + pv , can be dh= du + Pdv + vdp
This is all just dealing with mathematics , please teach me how to choose
Do you mean why did I put constant volume there? It means by keeping volume constant then only differentiate.
Thank
 
Outrageous said:
(∂s/∂P) at constant volume =1/T ×(∂u/∂T)at constant volume × (∂T/∂P) at constant volume

s(P,v)
Tds= du +pdv
h= u + pv
h(P,v)
u(P,v)
or other formula?
How am I going to choose ? Please guide

Thank

Have you considered using the Maxwell relations?

BiP
 
Outrageous said:
Do you mean why did I put constant volume there?
No, I mean take this equation: Tds= du +pdv
and turn it into an equation involving partial derivatives, v being constant.
 
Bipolarity said:
Have you considered using the Maxwell relations?

BiP

haruspex said:
No, I mean take this equation: Tds= du +pdv
and turn it into an equation involving partial derivatives, v being constant.

I am not really understand what is Maxwell ,
I only can get (∂s/∂P) at constant volume = (1/T)(∂h/∂P)constant volume -(v/T)
 
Outrageous said:
I only can get (∂s/∂P) at constant volume = (1/T)(∂h/∂P)constant volume -(v/T)
Please post your working to get that.
 
Trial
 

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This first , only that second deriavative
 

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  • #10
You need to follow BiP's advice and familurize yourself with the derivation and application of the Maxwell equations.
 

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