Question

You've packed a cube shaped cooler for the beach. Its 6 walls are made of 2 centimeter thick styrofoam and have lengths and heights of 40 centimeters each. If you were to fill it with 0 degree ice, how much ice would melt in 2.6 hours if the cooler was sitting in +35 C warm air. (use 0.035 for the k value of styrofoam and 334000 J/kg for the latent heat of fusion for ice.)

Answer 1

Thickness L = 2 cm =0.02 m

Area A ' = 40 cm x 40 cm = 0.4 mx0.4 m

           = 0.16 m ²

Total area of six faces A = 6 A '

                                    = 0.96 m ²

Time t = 2.6 hrs

          = 2.6 x60 min = 2.6 x60 x60 s

Temprature difference dT= 35 ^o C - 0 ^o C = 35 ^o C

Thermal conductivity of styrofoam K = 0.035 W /m ^oC

Rate of heat Q = KAdT / L

                      = 0.035 x0.96x35 /0.02

                      = 58.8 W

                      = 58.8 J /s

Heat received in time t is Q ' = Q t

                                           =(58.8 J/s) x2.6 x 60x60 s

                                           = 550368 J

Latent heat of fusion of ice L = 334000 J / kg

Amount ice melts m = Q ' / L

                               = 550368 J /(334000 J / kg)

                               = 1.647kg