How do I determine thermal conductivity in a physics problem when...?

Question

A Styrofoam box has a surface area of 0.76 m2 and a wall thickness of 2.0 cm. The temperature of the inner surface is 5.0°C, and the outside temperature is 24°C. If it takes 7.9 h for 5.0 kg of ice to melt in the container, determine the thermal conductivity of the Styrofoam.

Answer 1

Use Q/A = -k*dT/dx

where Q = heat per unit time flowing through wall, A = area of wall, dT = temeprature change from start to finish, and dx = thckness of wall.

Q is heat of fusion of water times mass of ice melted divided by time taken to melt ice

Q = mH/t where H= 334 J/gm

Then :

mH/(tA) = -k*dT/dx ---> dT = 24 - 5 = 19 C = 19 K --> the inside wall temp doesn't change until after the ice melts.

Solve for k : k = -mH*dx/(tA*dT) = -5*344x10^3*0.05/(7.9*3600*0.76*19) = 0.209 J/(K-s-m)

Answer 2

Q/t = ok A delta-T / thickness = (0.033 W /m ok) (pi) (0.one hundred twenty five m)^2 (40 ok) / (0.012 m) = seems to be around 5 watts, yet use calculator i assume the main to the low capacity is the extreme effectiveness of the froth.