Overview
Hypothermia (a lowering of the body's core temperature: link to Wikipedia article on hypothermia
) begins when the core temperature of a human drops to below 35.0 oC.
Question 1: For a human being with a body mass of 65.0 kg and an average heat capacity of 0.940 cal/g-oC and a starting temperature of 37.6 oC, what mass of ice must be melted and warmed to 35.0 oC in order to cool the person to 35.0 oC? (Assume the ice starts out at 0.00 oC so you don't have to include energy required to heat ice. But you do have to include the energy required to melt ice.)
Question 2: How many regular-sized Snickers candy bars must be consumed to offset this energy loss and warm the body back to 37.6 oC?
The main steps to this calculation are:
1. Calculate the net amount of heat released by cooling a 65.0 kg human from 37.6 oC to 35.0 oC.
2. Set up the calculation to show how much heat is required to melt a given mass of ice.
3. Set up the calculation to show how much heat is required to warm that same mass of ice from 0.00 oC to 35.0 oC.
4. Equate the total heat required to melt and warm the ice with the heat released by cooling and solve for the mass.
5. Find the calorie content in a Snickers bar (see here, for example: link to website of nutrition of candy
) and use that value to answer question 2. (Hint: Be careful and make sure you know the difference between a nutrition Calorie and a chemist's calorie!)
Thermodynamic properties of water and ice can be found in the textbook, Chemistry 2nd ed. in appendix E and appendix G.
Link to Appendix E in Chemistry 2nd ed.: Water Properties
Link to Appendix G in Chemistry 2nd ed.: Standard Thermodynamic Properties for Selected Substances