A 25.0 gram meteorite composed of iron is moving at a speed of 300 m/s and slams into the Earth.

Question

A 25.0 gram meteorite composed of iron is moving at a speed of 300 m/s and slams into the Earth. Assuming that 50% of the kinetic energy of the meteorite is converted into heat, by how much will the temperature of the meteorite increase? The specific heat of iron is 0.452 J/g C.

Answer 1

Set half of the kinetic energy K of the meteorite equal to mcΔT, and solve for ΔT.

 

c = 0.452 J/(g°C) = 452 J/(kg°C)  [work consistently with meters, Joules, and kg]

 

K = mv²/2 

 

K/2 = mcΔT

 

ΔT = K/(2mc) = (mv²/2) / (2mc) = v²/(4c) = (300 m/s)² / {4[452 J/(kg°C)]} ≅ 49.8°C