s a coffee enthusiast you wish to keep your coffee as hot as possible for as lon
ID: 1625720 • Letter: S
Question
s 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 24.0 °C how much more heat does the mug lose through conduction than from radiated energy? The thermal conductivity is not specified in this problem.
Answer should be: The mug loses heat by conduction _____ times more quickly than by radiation.
Explanation / Answer
As we know,
Energy loss by radiation = Emissivity x Stefan-Boltzmann Constant x ( T4 - Ts4 )
= Emissivity x Stefan-Boltzmann Constant x [(273+77.1)4 - (273+24.0)4 ]
= 0.730 x 5.67x10-8 x [(273+77.1)4 - (273+24.0)4 ]
= 299.77 W/m2
Energy Loss = [0.850 W/m °C (77.1 -24.0)°C]/ 0.0134
= 3368.28 W/m2
3368.28/ 299.77 = 11.236
= 11.236 times
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