Today is the birthday of
- William Shockley (1910-1989).
Today’s Problem
In the last problem we estimated the kinetic energy of a typical single falling snowflake to be \(1.5\times 10^{-6}\,\mathrm{J}\). If all of that energy goes into adding to its temperature, what is its final temperature when it starts out at a temperature of -10 degrees Celsius and its mass is 3 mg? Take the specific heat capacity at constant pressure to be \(2.0\,\text{kJ}/(\text{kg}\cdot^{\circ}\text{C})\).
Answer
The change in temperatue of the snowflake will be
\[\begin{eqnarray} \Delta T&=&\frac{\Delta E}{mC_p}\ &=&\frac{1.5\times 10^{-6}\,\text{J}}{(3\times 10^{-3}\text{g})(2.0\,\frac{\text{kJ}}{\text{kg}\cdot^{\circ}\text{C}})(\frac{1\,\text{kg}}{1000\,\text{g}})}\ &=&0.00025^{\circ}\text{C} \end{eqnarray}\]
So the temperature of the snowflake would rise from -10 degrees celsius to -9.99975 degrees celsius.
© 2026 Stefan Hollos and Richard Hollos