A 750-kg meteoroid happens to be composed of aluminum. When it is far from the E

Question

A 750-kg meteoroid happens to be composed of aluminum. When it is far from the Earth, its temperature is -15.5

A 750-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 16.0 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 times 105 J/kg, and the latent heat of vaporization is 1.14 times 107 J/kg.) degree C

Explanation / Answer

1/2(1/2mv^2)=mc(change in temperature from solid at -15.5C to fusion point of 660C)+mL1(Latent heat of fusion)+mc(660C to 2450C )+mL2(latent heat of vaporisation)+mc(2450C to final temperature)

where 1/2mv^2 is the kinetic energy of meteoroid equally divided by the meteoroid and earth,

c is the specific heat capacity of meteoroid

m is the mass of the meteoroid

L1 is latent heat of fusion and

L2 is latent heat of vaporisation

STEPS INVOLVED

1.meteoroid reaches melting point

2.Latent Heat is involved in melting of meteoroid

3.From melting point ,its temperature rises till it reaches boiling point

4.Latent Heat is involved in its vaporisation

5.From point of vaporisation it reaches its final temperature.

1/4*750*16000^2=750*1170*675.5+750*3.97*10^5+750*1170*1790+750*1.14*10^7+750*1170(x-2450)

==>x=44602.45C

Hence the final temperature of the meteoroid is 44602.45C

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