# Melting Problem

1. Dec 3, 2013

### icetea07

1. The problem statement, all variables and given/known data

You are going on a long trip in the summer with a dessert that must stay cold.
You have a cooler with the interior dimensions measuring 13 in x 8.5in x 11 in. The cooler has 1.75 in of polyurethane foam insulation. The dish is in a water tight container so food getting wet from melting ice is not a problem. The dish is a surprise so no one will open the cooler. The only concern is keeping the food on ice. You buy bags of ice with the average density of the bag at only 55% (due to air pockets). While the ice bags may be very cold in the freezer in which they were stored, by the time you get them out to your cooler, they have begun to melt. The average temperature in your vehicle is 80°F. The space occupied by the dish is relatively small and the dish itself has little overall effect on the problem.

1. How long will it take for the ice to completely melt if the cooler is completely filled with ice?
2. How long will it take for the ice to completely melt assuming you put a couple 8 lb bags of ice in the cooler?

(The themal conductivity we have to look up. I found it to be .03)

2. Relevant equations

Q=(KA(T-T0))/X

3. The attempt at a solution

Q=(.03(694 in.)(48°F))/1.75in Q=571.063

I believe I am supposed to also find H (i think that is what it is) and then divide them to get my time but i am not sure, and if so I have yet been able to figure out how to do so. Still working on that. Any help is appreciated.

2. Dec 3, 2013

### haruspex

In what units?
Q is usually used for a quantity of heat. What you are calculating is a rate of flow of heat (in what units)?
Depending on what 'H' means, and which way you divide, yes.