User:BSitzmann (WMF)/MCS/Test/Frankenstein

Frankenstein Castle is a medieval fortification on a spur above the village of Frankenstein, Rhineland-Palatinate in the Palatinate Forest in Germany. Its name derives from the local House of Frankenstein.

Some other section
Frankenstein is cool

Red link in da house!

More red links
A red link + Quotes' in" the' title" and red link

More links

 * Links partially italicized: Hindenburg disaster
 * Link to edit action using edit template:
 * Link to edit action using fullurl template [ edit2]

Pronunciation aids
Konjac

Media
[[media:Classical guitar scale.ogg|Sound]]

Math
Let q = (qx, qy, qz) and p = (px, py, pz) denote the position vector and momentum vector of a particle of an ideal gas, respectively. Let F denote the net force on that particle. Then the time-averaged potential energy of the particle is:

\begin{align} \langle \mathbf{q} \cdot \mathbf{F} \rangle &= \Bigl\langle q_{x} \frac{dp_{x}}{dt} \Bigr\rangle + \Bigl\langle q_{y} \frac{dp_{y}}{dt} \Bigr\rangle + \Bigl\langle q_{z} \frac{dp_{z}}{dt} \Bigr\rangle\\ &=-\Bigl\langle q_{x} \frac{\partial H}{\partial q_x} \Bigr\rangle - \Bigl\langle q_{y} \frac{\partial H}{\partial q_y} \Bigr\rangle - \Bigl\langle q_{z} \frac{\partial H}{\partial q_z} \Bigr\rangle = -3k_{B} T, \end{align} $$ where the first equality is Newton's second law, and the second line uses Hamilton's equations and the equipartition theorem. Summing over a system of N particles yields



3Nk_{B} T = - \biggl\langle \sum_{k=1}^{N} \mathbf{q}_{k} \cdot \mathbf{F}_{k} \biggr\rangle. $$

Conversions

 * 60 and 170 kg
 * 18 °C
 * 3.21 kg

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