Question

A hot cup of black coffee (85°C) is placed on a tabletop (22°C) where it remains. The surrounding room is at a temperature of 22°C. The cup is cylindrical in shape with a height of 15.0 cm and an outside diameter of 8.00 cm. The cup is made of ceramic with a thermal conductivity of 0.84 W/m°C. The outside of the cup has a temperature of 60°C and the cup is 6.0 mm in thickness. A slight breeze is blowing in the room.

What is the rate of heat loss due to convection from the top of the coffee? Use a convection coefficient of  1010  W/m2°CW/m2°C for the coffee's surface.

Give your answer as positive since we are calculating the magnitude of the rate of loss.

What is the rate of heat loss due to evaporation if the coffee evaporates at 0.001 grams/second?

Give your answer as positive since we are calculating the magnitude of the rate of loss.

What is the total rate of heat loss for the coffee?

Give your answer as positive since we are calculating the magnitude of the rate of loss.

If the rate of cooling is assumed to be constant, how long will the coffee take to reach a temperature of 25°C?

Answer 1

Outside radius (8)= 4cm = 48102m h = 15x10rem inner radius (ri) = 0.034m. a) Total rate of heat loss due to convection from the side of the cup o Latent heat of evoporation - 2.257 kJ/ig = 22573115. The rate of heat loss due to evo poration Q2 = 2257% 0.001 102= 2.257w Total rate of heat loss bor coffee 53.127W. dT dt T=kttc ta -60 (k = tive] (Required < time). = ka constant.