A styrofoam cooler (k = 0.030 W/(m middot degree C) has outside dimensions of 0.

Question

A styrofoam cooler (k = 0.030 W/(m middot degree C) has outside dimensions of 0.170 m times 0.390 m times 0.440 m, and an average thickness of 3.0 cm. How long will it take for 4.60 kg of ice at 0 degree C to melt in the cooler and reach the outside temperature of 24.0 degree C? The cooler is rectangular and box-shaped. A good way to estimate the effective surface area for heat transfer is to average the inner and outer surface areas. Another way is to use dimensions halfway through the styrofoam.

Explanation / Answer

k = 0.030 W/moc, delta T = 24 oC, d = 3.0 cm = 0.03 m

A = 2 * (0.17 * 0.39 + 0.39 * 0.44 + 0.44 * 0.17) = 0.6254 m2

Rate of heat transfer Q/t = kA(Thot - Tcold) / d = 0.03 * 0.6254 * (24 - 0) / 0.03 = 15 W

Energy required = 4.60 * 3.34 * 105 = 1536 kJ

Required time = 1536,400 / 15

= 102427 sec = 28.5 hr

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