Aperson puts a few apples into the freezer at -15°c to cool them quickly for guests who are about to arrive. initially, the apples are at a uniform temperature of 20°c, and the heat transfer coefficient on the surfaces is 8 w/m^2c. treating the apples as 9-cm-diameter spheres and taking their properties to be ρ=840 kg/m3, k-0.418 w/m"c, α =1.3 x 10^-7 m^2/s, cp=3.81 kj/kg."c, determine the center temperature of the apples in 1 hour.

To save energy, the air supply to a 2000 ft office has been shut off overnight and the room temperature has dropped to 40°f. in the morning, the thermostat is reset to 70°f and warm air at 120 f begins to flov in at 200ft'/min. the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct. the air pressure is nearly 1 atm everywhere. ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach 70°f. plot the room temperature as a function of time.