Rogue pastry chefs have developed a portable death ray which

Rogue pastry chefs have developed a portable \"death ray\" which they intend to use to bake calces from a distance. The radiation emission from the device can be approximated as that of a blackbody at 5000 K. To test its effectiveness, the beam is aimed at one side of a thin sheet of cake batter which has been placed in the center of a large room. (Naturally this experiment is being performed in outer space, so you can assume the cake is not touching any surfaces.) The walls of the room and ambient air are both at 300 K and the heat transfer coefficient inside the room is h = 10 W/m2 K. Assume that the cake batter has an emissivity of 0.9, and the following spectral properties: tau_lambda = {0.05 lambda

Solution

a) transissivity = 0.05*10*(5000- 300)

= 470 w

reflectivity = .6 + .2 0.1 * 0.05*10* (5000-300)

= 610 w

b) power = 5.67 * 10^-7 * e *A * T1^{4 -} T2 ⁴

= 467 W