As a master chef, chemical engineer, and employee of Pillsbury, you are devising a new devil's food cake mix. You would like to have some idea of how long to bake the thing and your only guideline is that you know the center of the cake must reach a temperature of at

You may assume a sheet cake \(0.33(1) \times 0.23(w) \times 0.025(d)\) initially. The heat-transfer coefficient in the oven is low, \(5 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\), and convective heat transfer occurs from both sides of the cake. How small a heat-transfer coefficient would we need to solve the problem using lumped capacitance? Comment on how long it would take to bake the cake.

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Density Thermal Conductivity Heat Capacity Cake Temperature (K) (kg/m) (W/m K) (J/kg K) 300 720 0.223 3300 340 575 0.175 2750 370 400 0.150 2250 410 280 0.121 1750