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\sect{Radiation from a 1D blackbody fiber}
Consider an optical fiber that has a length ${L}$. Its section area is ${A}$.
The fiber is in thermal equilibrium at temperature ${T}$.
Assume the fiber is a one dimensional medium for the electromagnetic
field. Regard the system as a 1D photon gas.
\begin {itemize}
\item[(a)]
What is the electromagnetic energy density per unit length?
\item[(b)]
What is the radiation pressure on each fiber end?
\item[(c)]
Assuming that the radiation is freely emitted from an end of the fiber,
find the energy flow per unit time.
\item[(d)]
What is the spectral distribution ${J(\omega)}$ of the emitted radiation?
\item[(e)]
What is the entropy and what is the heat capacity of the system?
\end {itemize}
You can use the following integral
\[\int_{0}^{\infty}\frac{x}{e^{x}-1}dx=\frac{\pi^{2}}{6}\]