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Tags atmosphere, earth, energy, friction, heat, iron, kinetic energy, latent heat, melt, melting, meteorite, physics, thermodynamics Difficulty Points 2 Language Type Quantity Last modified 1 month, 3 weeks ago Initial Version by Urs Zellweger (urs)	This Exercise is currently not added to any collections.	0

Exercise

An iron meteorite melts when it enters the Earth's atmosphere. If its initial speed outside of Earth's atmosphere was \SI{1.8}{\kilo\meter\per\second}, calculate the minimum temperature the meteorite could have had before it entered Earth's atmosphere. (Iron melts at \SI{1535}{\degreeCelsius}, its specific heat is \SI{450}{\joule\per\kilo\gram\per\kelvin} and its latent heat of fusion \SI{2.77e5}{\joule\per\kilo\gram}.)

Solution

If the iron meteorite melts, it must be heaten up to irons melting point ($\theta_f=\SI{1535}{\degreeCelsius}$) and then be melted. The energy for these two processes comes from the meteorites speed, hence: \begin{align} \Ekin &= Q\\ \Ekin &= Q_{\Delta} + Q_f\\ \frac12 mv^2 &= c \cdot m \cdot\Delta\theta + m\cdot L_f\\ \frac12 v^2 &= c \cdot(\theta_f-\theta_0) + L_f\\ \theta_0 &= \SI{-200}{\degreeCelsius} \end{align}

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