Material Science
posted by Joy on .
A polystyrene ice chest contains 3 kg of ice at 0 degrees Celsius. Triangle H for melting = 3.34 x 10 to the 5 power J/kg p = 1000 kg/m cubed, CP =4190 J/ (kg K). Heat transfer is limited by conduction (k=0.06W/m K)) from the outside wall at 30 degrees Celsius. This means that temperature within the ice chest is not a function of position. Assume the heat flux (J/(sec m squared) is the same through all walls: top, sides, bottom. The walls have thickness = 4 cm and total surface area = 2400 cm squared.
Calculate heat flux (J/ (sec m squared) at the walls.

T within wall = 0 deg C
T outside wall = 30 deg C
wall thickness = .04 m
Heat power flux in Watts per m^2 = .06 W/m deg (30 deg)/.04 m = 45 Watts/m^2
since a Watt is a Joule per second, that is the answer.
Now the real question, which should be part B, is how long until the ice is melted :)
45 Watts/m^2 * 2400 *10^4 m^2 = 10.8 Watts pouring out through the walls of the box
how many Joules to melt the ice?
3 kg *334000 J/kg = 10^6 Joules
so
10.8 Joules/second * T = 10^6 Joules
T = 92778 seconds to melt
or
92777/3600 = 26 hours to melt