As a coffee enthusiast you wish to keep your coffee as hot as possible for as lo

Question

As a coffee enthusiast you wish to keep your coffee as hot as possible for as long as possible. You wish to find the rate of heat loss of a typical coffee mug. Assume the mug to be a cylinder which has a lid made out of the same material as the rest of the cylinder, and the thickness of the walls is 1.00 cm. If the coffee in the mug is 79.2 °C and the room temperature is 22.4 °C how much more heat does the mug lose through conduction than from radiated energy.

Assume that the thermal conductivity of all sides of the mug is 0.919 W/m·C, that the mug has an emissivity of 0.760 and the Stefan-Boltzmann Constant is 5.67 × 10-8 W/m2·K4. Remember to properly convert all units and to include all surfaces of the mug.

Explanation / Answer

By radiation, the power loss is,

Pr = Ae(Tc4 - T4) = [0.760*5.67 × 10-8 *{352.24 - 295.44}] A = [334.94]A

By conduction, the power loss is,

Pc = kA(Tc - T)/t = {[0.919*{352.2 - 295.4}]/ 0.01}A = [5219.92]A

The ratio is,

Pc/Pr = [5219.92]A / [334.94]A

Pc = [15.58]Pr

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