OnTech, a San Diego startup company, has developed self-heating containers for meals and beverages. These containers will heat coffee to an optimal drinking temperature of 145 degrees F (63 degrees C) within minutes after pressing a button, and the containers are designed to keep beverages hot for 20 minutes (and warm for about an hour).
When you’re about ready for coffee, turn the can over and remove the “tamper proof foil”. Push the “activation button” to break the “foil seal." Gravity causes water (“heat generating liquid”) to flow from the “water container” into the “heat generating material”, which is calcium oxide (=3.34 g/cm3; =42 J/K/mol). Water reacts with calcium oxide, producing heat and calcium hydroxide (=2.21 g/cm3; =87.5 J/mol/K):
(The “internal heat generation cone” contains no calcium oxide; it is a finned heat transfer surface that is designed to expedite heat transfer to the coffee by increasing the heat transfer surface area. You may assume that this finned cone requires negligible volume since it’s comprised of very thin, extended surfaces.)
After five seconds, turn the can over. Wait about six to eight minutes, pop the top, and enjoy your hot coffee without ever leaving your desk.
You must design a standard 16-oz (470 mL) beverage container to hold coffee and all components of the heat source (water, calcium oxide). Check the feasibility of this concept by calculating the largest volume of coffee that the container can hold while still meeting the requirement that the coffee be heated from room temperature to 145 degrees F (63 degrees C). Does this volume of coffee seem reasonable for a single serving? (You do not need to worry about the rate of heat transfer at this time; so you don’t need to consider the requirement that the coffee reaches 145 degrees F (63 degrees C) in six minutes.)