Question

Approximately how long should it take 9.4 kg of ice at 0∘C to melt when it is placed in a carefully sealed Styrofoam ice chest of dimensions 25 cm × 35 cm × 55 cm whose walls are 1.8 cm thick?

Assume that the conductivity of Styrofoam is double that of air and that the outside temperature is 31 ∘C. Express your answer to two significant figures and include the appropriate units.

Answer 1

m = mass of the ice = 9.4 kg

L = latent heat of fusion of ice to water = 334000 J/kg

Heat of melting is given as

Q = mL

k = thermal conductivity = 0.046

Area is given as

A = area = 2[(0.25) (0.35) + (0.35) (0.55) + (0.55) (0.25)] = 0.835 m2

T = temperature difference = 31 - 0 = 31 oC

x = thickness of the wall = 1.8 cm = 0.018 m

t = time taken

Using the equation

Q/t = k A T/x

mL/t = k A T/x

(9.4)(334000)/t = (0.046) (0.835) (31)/0.018

t = 47461.4 sec