What do the subscripts in Maxwell's equations mean

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SUMMARY

The subscripts in Maxwell's equations indicate which thermodynamic variables are held constant during differentiation. For example, in the expression \(\left(\frac{\partial T}{\partial V}\right)_S\), the subscript \(S\) signifies that entropy is held constant while differentiating temperature with respect to volume. This notation is crucial for understanding thermodynamic relationships and is more commonly used in physics than in mathematics. The discussion clarifies that while partial derivatives imply the constancy of other variables, the explicit notation helps in the derivation of thermodynamic identities.

PREREQUISITES
  • Understanding of thermodynamic concepts such as temperature, volume, and entropy.
  • Familiarity with partial derivatives and their notation in calculus.
  • Knowledge of Maxwell's relations and their significance in thermodynamics.
  • Basic grasp of thermodynamic identities and their derivations.
NEXT STEPS
  • Study the derivation of Maxwell's relations in thermodynamics.
  • Learn about the implications of holding variables constant in partial derivatives.
  • Explore the thermodynamic identity and its applications in physics.
  • Review examples of how subscripts are used in various thermodynamic equations.
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Students of physics, particularly those studying thermodynamics, as well as educators and anyone seeking a deeper understanding of Maxwell's equations and their applications in physical sciences.

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Homework Statement


http://en.wikipedia.org/wiki/Maxwell_relations

I am confused about the subscripts next to the partial derivatives.
[tex]\left(\frac{\partial T}{\partial V}\right)_S =<br /> -\left(\frac{\partial p}{\partial S}\right)_V\qquad=<br /> \frac{\partial^2 U }{\partial S \partial V}[/tex]
What does the S mean after the first partial? Does it mean that this equation is only true when entropy is held constant? I thought the point of a partial derivative was to hold constant all other quantities except the one that you differentiate w.r.t?

Homework Equations


The Attempt at a Solution

 
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In general, the subscripts denote which parameters are held constant.
 
You're right, it is implied that all other things are held constant when taking partial derivatives... but it's often written in out in physics whereas not so much in math. Mostly it's written down (in my opinion) in the derivations of these relations using the thermodynamic identity.
 

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