Question

The Styrofoam™ box in is used to keep drinks cold at a picnic. The total wall area (including the lid) is 0.80 m^2, and the wall thickness is 2.0 cm. The box is filled with ice and cans of cola, keeping the inner surface at 0 ∘C. What is the rate of heat flow into the box if the temperature of the outside surface is 30 ∘C? How much ice melts in one day (24 h)?

This same Styrofoam™ cooler is sitting in the sun, and the outside temperature reaches 38 ∘C. How much time passes before the 8 lb of ice is completely melted?

Answer 1

PART 1:

The value of k is 0.01 W/mK.

We know

So, the rate of heat flow is 12 J/s.

In one day the total heat flow is

The heat of fusion of ice is 334 kJ/kg

So, the total ice melt in one day is

PART 2:

Now, the outside temperature changes

And the rate of heat flow now is

The mass of ice melted is

The energy required to melt the ice is

So, the time taken to melt the ice is

So, it would take 22.15 hour to melt 8 lb of ice in the outside temperature.