A 900 -kg meteoroid happens to be composed of aluminum. When it is far from the

Question

A 900-kg meteoroid happens to be composed of aluminum. When it is far from the Earth, its temperature is -11.0

A 900-kg meteoroid happens to be composed of aluminum. When it is far from the Earth, its temperature is -11.0 degree C and it moves at 12.0 km/s relative to the planet. As it crashes into the Earth, assume the internal energy transformed from the mechanical energy of the meteoroid-Earth system is shared equally between the meteoroid and the Earth and all the material of the meteoroid rises momentarily to the same final temperature. Find this temperature. (Assume the specific heat of liquid and of gaseous aluminum is 1 170 J/kg · degree C, the melting point is 660 degree C, the boiling point is 2 450 degree C, the latent heat of fusion is 3.97 105 J/kg, and the latent heat of vaporization is 1.14 107 J/kg.)

Explanation / Answer

mass of meteoroid M = 900 kg

the initial temperature is T1 = -11.0 oC

let the final temperature be T2

speed of meteoroid v = 12.0 km/s = 12.0 x 10^3 m/s

we know from the relation

M x s x (T2 - T1) + M x Lf = (1/2)M x v^2

where s = 1170 J/kg.oC and Lf = 3.97 x 10^5 J/kg

solving the above equation for T2

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