What do the subscripts in Maxwell's equations mean

AI Thread Summary
The subscripts in Maxwell's equations indicate which variables are held constant during differentiation. In the equation provided, the "S" signifies that entropy is held constant when taking the partial derivative of temperature with respect to volume. This notation is common in physics to clarify which parameters are fixed, even though in mathematics, it is often implied. Understanding this can help clarify the relationships expressed in thermodynamic identities. The discussion emphasizes the importance of recognizing these conventions in the context of thermodynamics.
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Homework Statement


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

I am confused about the subscripts next to the partial derivatives.
\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}
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?

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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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