Morning Coffee

Physics at 11:20 is my first class of the day, and I always pour myself a cup of coffee at home before heading up the hill to class.  The cups we have at the house are made of styrofoam, which I have noticed does not do the best job at keeping my coffee warm throughout all of my classes during the day. I looked up to emissivity constant of polystyrene and found it to be 0.60. With this information, and making the assumption that the entire cup (including the top) is made of styrofoam, I want to find out how much heat is lost from my coffee from the time I pour it until the end of physics class about 1 hour later. The net flow of radiation is defined as: Q/T = eσA(T1^4 - T2^4). I assumed the cup is a perfect cylinder and found the surface area to be .034 meters squared. The energy loss per unit time is calculated as: Q/T= (.6)(5.67x10^-8)(.034)(100^4-21^4)= 1.15 watts or 1.15 joules per second. Over the course an hour, that is 4.1 kJ of heat lost from radiation over the course of physics lecture.