This is not an exponential decay problem.
Calculate the rate that heat enters the cooler. Heat will flow in at a rate
dQ/dt = (Surface Area)*k/(thickness)
where k is the thermal conductivity of Styrafoam (aka polyurethane foam). You will need to find a value for the thermal conductivity k, and use the appropriate units, such as cal/(sec*inch*degC).
Then calculate the amount of heat needed to melt the 3 kg of ice, while it (and the soda) remain at 0 C.
Q = (3000 g)*80 (cal/g) = 240,000 cal
The time required is Q/(dQ/dt)
Hi,
I have this question, except I don't know to solve. I think it has something to do with exponential decay and heat flow, but I would like some more help.
"3 kg of ice and a 12-pack of ice-cold soda are placed in a 25" x 25" x 40" (outside dimensions)
Styrofoam™ cooler with 1" thick sides.
How long will its contents remain at 0° C if the outside is a
sweltering 35° C? Assume no condensation forms on the outside of the cooler. Ignore the effects of convection and conduction of the air inside."
Thanks!
1 answer