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\begin{enumerate}
\item Radiation in electrostatic levitation

  Electrostatic levitation is used for property measurements in a pure liquid,
  with its containerless nature removing a major possible source of
  contamination.

  Below is a picture of a simplified levitator, with a charged droplet of the
  test liquid suspended exactly centered between two square plates.

  \begin{center}
    $\ $\pdfximage{levitate-es.png}\pdfrefximage\pdflastximage$\ $
  \end{center}

  Data:
  \begin{itemize}
  \item Plates' emisivity: 0.8
  \item Droplet emissivity: 0.5
  \item Droplet diameter: 0.5 cm (sphere surface area is $4\pi R^2=\pi d^2$)
  \end{itemize}

  \begin{enumerate}
  \item Considering the droplet surface as $S_1$, and the upper and lower plate
    surfaces facing the droplet collectively as $S_2$, calculate the viewfactor
    from the droplet to the upper and lower plates $F_{12}$.  (Hint: think of
    the plates as sides of a cube.)

  \item Calculate the viewfactor from the plates to the droplet.

  \item Using a graph, calculate the viewfactor $F_{22}$ (which is equal to the
    viewfactor from one plate to the other), {\em not} including the influence
    of the droplet ({\em i.e.} as if it weren't there).

  \item If the droplet is at 800 K, and the plates at 1000 K, calculate the
    total power radiated in each direction ({\em i.e.} $Q_{12}$ from droplet to
    plates, $Q_{21}$ from plates to droplet).

  \item If its actual thermal conductivity as measured in the levitator ({\em
      e.g.} by a laser flash technique) is 20\% higher than that predicted by
    the Wiedmann-Franz law for electronic heat conduction, what other heat
    conduction mechanism could be active (name one)?
  \end{enumerate}
\end{enumerate}
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