At a picnic, a Styrofoam cup contains lemonade and ice at 0 degree C. The thickness of the cup is 2.0*10^-3m, and the area is 0.016 m^2. The temperature at the outside surface of the cup is 35 degree C. The latent heat of fusion for ice is 3.35*1065 J/kg. What mass of ice melts in one hour?

Please give some hints to do it!Thanks!

You need the heat transfer coefficient of styrofoam. It is about .01 watts meters/deg

call area of foam A = .016 m^2
call temperature difference across styrofoam = 35 - 0 = 35 deg C
call thickness of foam t = 2*10^-3 m
then heat gained through foam = (k A/t)((35-0)
heat gain rate watts = (.01*.016/.002)(35)

That watts * time in seconds = Joules
so that times 3600 = Joules gained to melt ice in one hour. Now kg melted = Joules gained/ heat of fusion in Joules/ kilogram

By the way, I think heat of fusion is about 3.33 * 10^5 Joules/kg. You have a typo.

I don't really get the last part...so that times 3600 = Joules gained to melt ice in one hour. Now kg melted = Joules gained/ heat of fusion in Joules/ kilogram

Please explain.

(.01*.016/.002)(35)joules/s *3600 s = X kg ice * 3.33*10^5 Joules/kg ice melt

To find the mass of ice that melts in one hour, we need to calculate the amount of heat transfer that occurs between the hot exterior surface of the cup and the cold interior containing the ice. This heat transfer will be used to melt the ice.

Here are some steps you can follow to solve the problem:

1. Calculate the heat transfer through the Styrofoam cup using Fourier's Law of heat conduction. The formula for heat transfer through a solid object is Q = (k * A * ΔT) / d, where Q is the heat transfer, k is the thermal conductivity of the material (Styrofoam), A is the area of heat transfer, ΔT is the temperature difference, and d is the thickness of the material (the cup). In this case, you know the values for A, ΔT (35°C - 0°C), and d, so you need to find the value of thermal conductivity (k) for Styrofoam.

2. Calculate the energy required to melt the ice. The formula for heat transfer during a change of phase (melting or freezing) is Q = m * L, where Q is the heat transfer, m is the mass of the substance (in this case, the ice), and L is the latent heat of fusion for the substance (given as 3.35 * 10^6 J/kg). You need to find the value of mass (m) of the ice.

3. Since we know the equation for heat transfer through the Styrofoam cup (step 1) and the equation for heat transfer during the melting of ice (step 2), we can create an equation by equating the two values of Q and solve for the mass of ice (m).

4. Once you have the mass of ice, you can calculate the mass of ice that melts in one hour. Remember that the problem statement gives the temperatures at the start of the picnic, so you'll need to account for the time it takes for the heat transfer to occur.

By following these steps, you should be able to find the mass of ice that melts in one hour at the given picnic scenario.