Thermodynamics Problem?

Question

At a picnic, a Styrofoam cup contains lemonade and ice at 0°C. The thickness of the cup is 2.0 10-3 m, and the area is 0.016 m2. The temperature at the outside surface of the cup is 34°C. The latent heat of fusion for ice is 3.35 105 J/kg. What mass of ice melts in 1 hour?

Answer 1

You are dealing with a simplified problem in heat conduction:
http://en.wikipedia.org/wiki/Heat_conduction

Since the inside of the cup stays at the constant temperature of 0 until all the ice is melted, all the heat that is conducted through the styrofoam comes from the melting of the ice.

The basic heat conduction equation tells you the rate of heat transfer. (Though you need the conductivity of styrofoam. The figure for extruded polystyrene should be good enough:
http://en.wikipedia.org/wiki/List_of_thermal_conductivities
)


You know the time, so you know the total heat.

When ice melts, it releases about 80 Cal/gram:
http://sol.sci.uop.edu/~jfalward/specificandlatentheats/specificandlatentheats.html

So you can figure out how many grams have to melt to supply the required energy.