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====== Maxwell Relations ======

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===== In-class Content =====

====Lecture: Maxwell Relations (?? minutes)====
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==Lecture notes from Dr. Roundy's 2014 course website:==
In the Interlude, we learned that mixed partial derivatives are the same, regardless of the order in which we take the derivative, so
$$\left(\frac{\partial \left(\frac{\partial f}{\partial x}\right)_y}{\partial y}\right)_x=\left(\frac{\partial \left(\frac{\partial f}{\partial y}\right)_x}{\partial x}\right)_y$$
$$\frac{\partial^2 f}{\partial x \partial y}=\frac{\partial^2 f}{\partial y \partial x}$$
In the Interlude we found a Maxwell relation from the energy conservation law:
$$dU = F_1dx_1 + F_2dx_2$$
$$\left(\frac{\partial \left(\frac{\partial U}{\partial x_1}\right)_{x_2}}{\partial x_2}\right)_{x_1}=\left(\frac{\partial \left(\frac{\partial U}{\partial x_2}\right)_{x_1}}{\partial x_1}\right)_{x_2}$$
$$\left(\frac{\partial F_1}{\partial x_2}\right)_{x_1}=\left(\frac{\partial F_2}{\partial x_1}\right)_{x_2}$$
As you know, in thermodynamics, partial derivatives are often physically measurable quantities. In such a case, their derivatives are also be measurable quantities that we often care about.

In your groups, consider mixed partial derivatives of the thermodynamic potential assigned to you, to derive a Maxwell relation. **[GROUP]**

====Activity: Seeking the right Maxwell Relation====
[[..:..:activities:eeact:eethermopartials|Seeking the right Maxwell Relation]]

**Activity Highlights**
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=====Homework for Energy and Entropy=====
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