A metal coffee mug and a ceramic coffee mug each initially contain 250g of coffee at 90∘C. The mugs are placed on a counter in a room whose air temperature is 22∘C.
Relevant measured properties:
• Metal mug: side-wall thickness 2.0mm, effective surface area (excluding top) 0.025m2, thermal conductivity of wall material km=15W⋅m−1⋅K−1, surface emissivity εm=0.08.
• Ceramic mug: side-wall thickness 5.0mm, same effective surface area 0.025m2, thermal conductivity kc=1.4W⋅m−1⋅K−1, surface emissivity εc=0.90.
Assume the coffee temperature is uniform within each mug at all times and that energy is lost only through the cylindrical wall surfaces; the tops are covered. Neglect convection and treat the room surfaces as large, isothermal surroundings at 22∘C.
(a) Calculate the initial rate at which energy leaves the coffee inside the metal mug through conduction across the wall.
(b) Using appropriate physical reasoning, compare the initial radiative energy-loss rate from the coffee in the metal mug to that from the coffee in the ceramic mug. No numerical calculation is required.
(c) Which mug will cool to 60∘C first? Construct a qualitative argument that weighs the competing influences of conduction and radiation for each mug.