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 1.17 cm. If the coffee in the mug is 77.1 °C and the room temperature is 24.8 °C how much more heat does the mug lose through conduction than from radiated energy. See the hint below for important constants. The mug loses heat by conduction ____ times more quickly than by radiation.

Explanation / Answer

rate of heat transfer H = dQ/dt = KA(T2-T1)/L

where K = coeffficient of thermal conductivity

A = area

T2-T1 = change of temperartue

so here k = 0.85 Wm/C

so

Q/t = 0.85 * A *(77.1-24.8)/(0.0117* 0.0117)

Q/t = 3247.50 * A J/s

heat oss by radiation

Q/t = A e sigma (Th^4 - Te^4)

Q/t = A * 5.67 e -8 * 1 * (77.1+273)^4 - (24.8+273)^4

Q/t = 405.88 A

so ration = 324750/405.88 = 8

so heat loss by conduction is 8 times the heat loss by radiation

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