A 950-kg meteoroid happens to be composed of aluminum. When it is far from the E
ID: 1298359 • Letter: A
Question
A 950-kg meteoroid happens to be composed of aluminum. When it is far from the Earth, its temperature is -17.0 degree C and it moves at 14.5 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 x 10^5 J/kg, and the latent heat of vaporization is 1.14 x 10^7 J/kg.) ________ degree CExplanation / Answer
Given that
mass of meteroid m = 950 kg
temperature t = -170 c
speed 14.5 km/s
specific heat = 1170 J/kg.c
the lost of mechanical energy is
=( 1/2) mvi2 + GME/RE
= ( 1/2) 950 ( 14.5 x 10 ^3 m/s)^2 + (6.67 x 10^-11) ( 5.98 x 10^24 ) ( 950 )/ (6.37 x 10^6)
= 9.987 x 10^10 J + 5.948 x 10^10 J
= 1.5935 x 10^11 J
one half becomes extra internal energy in hte aluminimum ?Eint = 7.967 x 10^10 J to raise temperature to the mealting point requires energy
mc?T = 950 kg ( 900 J/kg.c) (660 -(- 17) = 578835000 J = 5.78835 x 10^8 J
to melt mL = 950 x ( 3.97 x 10 ^5 kg) = 377150000 J = 3.7715 x 10^8 J
to raise it to be the boiling point
mc?T = 950 ( 1170 ) ( 2450 - 660 ) = 1989585000 J = 1.989585 x 10^9 J
to boil it mL = 950 kg ( 1.14 x 10^7 J/kg) = 1.083 x 10 ^10 J
then
7.967 x 10^10 J = [ 5.78835x10^8 J+3.7715x10^8J+1.989585x10^9J+1.083x10^10J]+ 950(1170)( T(f) - 2450 ) J/c
7.967 x 10^10 J = [1.377557x10^10J]+ 950(1170)( T(f) - 2450 ) J/c
T(f) = 61734 0C
T(f) = 6.1734 x 10^4 0C
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.