Consider a thin suspended hotplate that measures 0.2 m × 0.2 m. the isothermal plate has a mass of 3.75 kg, a specific heat of 2770 j/kg·k, and a temperature of 275°c. the ambient air temperature is 25°c and the surroundings temperature is 25°c. if the convection coefficient is 6.4 w/m2·k and the emissivity of the plate is ɛ= 0.42, determine the time rate of change of the plate temperature, d⁢t/d⁢t , when the plate temperature is 275°c. evaluate the magnitude of the heat losses by convection and by radiation.

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 the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct.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.