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.

Part A

Part complete

What is the rate of heat loss due to radiation from the outside of the cup if the outside surface is 60°C? Assume that the emissivity of the ceramic is about 0.95.

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

Answer is 9.6

Part B

Part complete

What is the rate of heat loss due to radiation from the coffee itself?

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

Answer is 2.5W

Part C

Part complete

What is the rate of heat loss due to conduction through the bottom of the cup?

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

44.1W

Part D

Part complete

What is the rate of heat loss due to convection from the side of the cup? Use a convection coefficient of  10

10 W/m^2°C for the cup's surface.

Answer is 14.4W

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

Part E

What is the rate of heat loss due to convection from the top of the coffee? Use a convection coefficient of  10

10  W/m^2°C

W/m2°C for the coffee's surface.

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

Part F

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.

Part G

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.

Part H

Part complete

What heat must be removed from 200 grams of coffee to cool it to 25°C? You may assume that the specific heat capacity of coffee is the same as water.

Part I

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

Given that, height = 150m Diameter 28cm Temperature i Ti = 65+273 = 383k Part A we know, A=2170h = 283.148x162 x 15x162 = 377. xlouna The rate of heat loss due to radiation , P=REA (1,4+T34) -5.67X103)(0-95) (377X10/) (1333744/295)4 -966 Part Bi The rate ob heat loss due to radiation (910m lobble. PPDEA 6,14-T34) 55.6715$ xa1958 (1148313Y) (1833)4_C245)) - 24 Parte; P=KA(TI-T2) x 872699) ((85–22) 64103 = 44.30 Pastas The date of heat loss due to conveCHON Á) pahe Ady = 108377X10 (8522) = 2318 W