Working with Maxwell's equations

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    Maxwell's equations
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Discussion Overview

The discussion revolves around the mathematical manipulation of Maxwell's equations, specifically focusing on a thermodynamic identity involving partial derivatives. Participants are trying to understand the relationships between temperature, pressure, and internal energy in the context of thermodynamics.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents a mathematical expression involving partial derivatives and seeks clarification on the substitution steps leading to the conclusion (δT/δV)s = - (δP/δS)v.
  • Another participant expresses confusion regarding the notation used in the equations and provides an alternative formulation of the first law of thermodynamics, suggesting different interpretations of the variables involved.
  • Several participants indicate a lack of understanding regarding the manipulation of differential expressions and the notation used, questioning its clarity and correctness.
  • One participant suggests that the notation is problematic and asks if the final result can be derived from their previously stated equations.
  • A later reply indicates that one participant has resolved their confusion independently.

Areas of Agreement / Disagreement

Participants generally express confusion and disagreement regarding the notation and mathematical steps involved in the discussion. No consensus is reached on the clarity of the expressions or the validity of the manipulations presented.

Contextual Notes

Limitations in understanding arise from the notation and the manipulation of differential expressions, which some participants find unclear. The discussion does not resolve these issues, leaving the mathematical steps and assumptions open to interpretation.

AndrewBworth
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Hello all - I've been trying to work out an example from a book, and I don't quite understand the math.

show that (δT/δV)s = - (δP/δS)v

solution (δ/δV (δU(S,V)/δS)v)s = (δ/δS(δU(S,V)/δV)s)v
(δ/δV (δ(TdS - PdV)/δS)v)s = (δ/δS(δ(TdS-PdV)/δV)s)v
(δT/δV)s = -(δP/δS)v

I don't understand the substitution or the last step
 
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I don't understand the notation. The way I learned it is as follows:

##dU=TdS-PdV##

We must also have that:

$$dU = \left(\frac{\partial U}{\partial S}\right)_VdS+\left(\frac{\partial U}{\partial T}\right)_SdV$$

Therefore, comparing both equations, we have:

$$T=\left(\frac{\partial U}{\partial S}\right)_V$$
$$-P=\left(\frac{\partial U}{\partial T}\right)_S$$
 
Right I don't understand it either they've inserted the differential expression into a partial fraction I don't know how to work with it.
 
AndrewBworth said:
Right I don't understand it either they've inserted the differential expression into a partial fraction I don't know how to work with it.
So their notation in hinky. Can you get to the final result from my last two equations?

Chet
 
Sure no sweat.
 
Ah I figured it out
 

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