A 960.0 g iron meteor impacts the earth at a speed of 1,268.0 m/s. If its kinetic energy is entirely converted to heat of the meteorite, what will the resultant temperature rise be? (The specific heat for iron is 0.113 cal/g•K.)

The resultant temperature rise is 274.7 ⁰C

Explanation:

If the iron meteor kinetic energy is entirely converted to heat of the meteorite, then ΔKE = ΔThermal energy

ΔKE = ¹/₂ mv²

where;

m is mass in kg

v is velocity in m/s

ΔKE = ¹/₂ × 0.96 ×(1268)² = 771755.52 J = 184.454 cal

ΔThermal energy = mcΔT

where;

m is mass in g

c is the specific heat for iron = 0.113 cal/g•K

ΔT change in temperature or resultant temperature rise

Since, ΔKE  = mcΔT

184.454 cal = 960 g × (0.113 cal/g•K) × ΔT

184.454 cal = (108.48 cal/K)ΔT

ΔT

ΔT = 1.7 K = (237 + 1.7)⁰C = 274.7 ⁰C

Therefore, the resultant temperature rise is 274.7 ⁰C