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% (C) 2010 by Eugeniy Mikhailov, <evgmik@gmail.com>
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\usepackage{listings}
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\begin{document}
\newcommand{\problem}[1]{%
	{\flushleft  \bf #1\\}
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\newcommand{\hw}[1]{%
	\begin{center}
		\Large  \bf Homework #1%
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}
\newcommand{\mat}[1]{% matlab code
{\color{blue}\texttt{#1}}%
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\hw{08}

\problem{Problem 1 (5 points)}
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Using Maxwell-Boltzmann distribution and assuming temperature of the sun to
be $10^7$~K estimate fraction of the hydrogen atoms capable to penetrate
the Coulomb barrier at 1~fm.

\problem{Problem 2 (5 points)}
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Assuming density of sun  to be 1300~kg/m$^3$ and heat capacity  of it to be
the same as  for water (per kg).  Estimate how much temperature  of the Sun
would  raise as  result  of calculated  above fraction  of  hydrogen to  be
converted  to helium.  Is  it  enough to  overcome  Coulomb  barrier for  a
hydrogen atom with average thermal energy?

\problem{Problem 3 (5 points)}
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Derive formula for the radiation pressure
\begin{equation}
	P=\frac{1}{3}a T^4
\end{equation}
and show that $a=4 \sigma/c$


\problem{Problem 4 (5 points)}
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Using Maxwell-Boltzmann distribution derive the formula for the ideal gas
pressure $P=n k_B T$.


\problem{Problem 5 (5 points)}
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What should  happen with pressure  when all  hydrogen will be  converted to
helium? How much  higher should be the temperature  to maintain hydrostatic
equilibrium assuming that the rest of the system does not change? Disregard
the ionization  and assume that  Sun consists only  of helium at  the final
stage.

\problem{Problem 6 (5 points)}
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Assuming mean molecular weight $\mu = 0.62$ and $\rho = 1300$ kg/m$^3$ find
at what temperature radiation pressure equals to ideal gas pressure.




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\end{document}
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