A 800 -kg meteoroid happens to be composed of aluminum. When it is far from the

Question

A 800-kg meteoroid happens to be composed of aluminum. When it is far from the Earth, its temperature is -15.5C and it moves at 13.5 km/s relative to the planet. As it crashes into the Earth, assume the internal energy transformed from the mechanical energy of the meteoroidEarth 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

A 800-kg meteoroid happens to be composed of aluminum. When it is far from the Earth, its temperature is -15.5 degree C and it moves at 13.5 km/s relative to the planet. As it crashes into the Earth, assume the internal energy transformed from the mechanical energy of the meteoroidEarth 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 middot 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 times 105 J/kg, and the latent heat of vaporization is 1.14 times 107 J/kg.)

Explanation / Answer

initial KE of meteoriod = 0.5*m*v^2 = 0.5*800*(13500)^2
= 7.29*10^10 joule

energy for melting = 800*1170*(660+15.5) + 800*3.97*10^5
= 949868000 joule

energy for boiling = 800*1170*(2450-660) + 800*1.14*10^7
= 1.08*10^10 joule

now,
let final temp is T
so,

(7.29*10^10/ 2) - 949868000 - 1.08*10^10 = 800*1170*(T - 2450)
=> T = 28843.90

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