A 6.5-g iron meteor hits Earth at a speed of 295 m/s.If its kinetic energy is entirely converted to the thermal energy of the meteor,by how much will its temperature rise? The specific heat of iron is 113 cal/kg ∙ C°,and 1 cal = 4.186 J.

Question

Quizplus · Accepted Answer

The kinetic energy (KE) of the meteor is given by $ \frac{1}{2}mv^2 $, where $ m $ is the mass in kilograms and $ v $ is the velocity in meters per second. First, convert the mass to kilograms: $ 6.5 \, \text{g} = 0.0065 \, \text{kg} $. Then, calculate the kinetic energy: $ KE = \frac{1}{2} \times 0.0065 \, \text{kg} \times (295 \, \text{m/s})^2 = 281.5125 \, \text{J} $.To find the temperature rise ($ \Delta T $), use the formula $ \Delta T = \frac{Q}{mc} $, where $ Q $ is the thermal energy (equal to the kinetic energy here), $ m $ is the mass in kilograms, and $ c $ is the specific heat capacity in J/kg°C. First, convert the specific heat capacity from cal/kg°C to J/kg°C: $ 113 \, \text{cal/kg°C} = 113 \times 4.186 \, \text{J/kg°C} = 473.018 \, \text{J/kg°C} $.Then, calculate the temperature rise: $ \Delta T = \frac{281.5125 \, \text{J}}{0.0065 \, \text{kg} \times 473.018 \, \text{J/kg°C}} = 92.0 \, \text{C°} $.

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