posted by Alex on .
Ice of mass 11.0 kg at 0.00° C is placed in an ice chest. The ice chest has 3.00 cm thick walls of thermal conductivity 1.00 10-5 kcal/s · m · C° and a surface area of 1.25 m2.
(a) How much heat must be absorbed by the ice before it melts?
(b) If the outer surface of the ice chest is at 29.0° C, how long will it take for the ice to melt?
Q = r•m =335000•11 = 3.685•10^6 J,
where r is the heat of fusion.
q = α•(ΔT/Δx)•A,
where q is the heat flow per unit time,
α is åðó thermal conductivity,
α =1•10^5 kcal/s • m • C° =
=0.041868 J/s • m • C°,
ΔT is the temperature driving force,
Δx is the thickness of the walls,
and A is the surface area,
q = 0.041868•(29/0.03) •1.25 =
t = Q/q = 3.685•10^6/50.59 = 7.28•10^4 s = 20.23 h.