A large cylindrical coffee pot in a coffee shop filled with 10.0 kg of hot coffee at temperature T = 95.0 ° C rests on a wooden table.  The steel pot has radius r = 8.00 cm and height h = 50.0 cm and an emissivity e = 0.600.  See figure. Assume that all heat loss is radiative through the side and top of the pot, given that wood is a relatively poor thermal conductor.  The coffee shop ambient temperature T = 20.0 ° C. a) Find the rate at which the coffee losses heat. b) Assuming constant heat loss rate, what is the coffee temperature after 10.0 minutes have elapsed?   Cw = 4.19 x 103 J/kg °C, ρw = 1.00 x 103 kg/m3,                  σ = 5.67 x 10 -8 W/m2 K4

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A large cylindrical coffee pot in a coffee shop filled with 10.0 kg of hot coffee at temperature T = 95.0 ° C rests on a wooden table.  The steel pot has radius r = 8.00 cm and height h = 50.0 cm and an emissivity e = 0.600.  See figure. Assume that all heat loss is radiative through the side and top of the pot, given that wood is a relatively poor thermal conductor.  The coffee shop ambient temperature T = 20.0 ° C. a) Find the rate at which the coffee losses heat. b) Assuming constant heat loss rate, what is the coffee temperature after 10.0 minutes have elapsed?   Cw = 4.19 x 103 J/kg °C, ρw = 1.00 x 103 kg/m3,                  σ = 5.67 x 10 -8 W/m2 K4                                                                                                                                                                                                                    

6. A large eylindrical coffee pot in a coffee shop filled with 10.0 kg of hot coffee at
temperature T = 95.0 °C rests on a wooden table. The steel pot has radius r=8.00 em and
height h = 50.0 cm and an emissivity e- 0.600. See figure. Assume that all heat loss is
radiative through the side and top of the pot, given that wood is a relatively poor thermal
conductor. The coffee shop ambient temperature T= 20.0 ° C. a) Find the rate at which
the coffee losses heat. b) Assuming constant heat loss rate, what is the coffee temperature
after 10.0 minutes have elapsed? C.-4.19 x 10' J/kg °C, pn = 1.00 x 10' kg/m',
a = 5.67 x 10 W/m K
%3D
%3D
Figure P6
Coffee Pot
Table
Transcribed Image Text:6. A large eylindrical coffee pot in a coffee shop filled with 10.0 kg of hot coffee at temperature T = 95.0 °C rests on a wooden table. The steel pot has radius r=8.00 em and height h = 50.0 cm and an emissivity e- 0.600. See figure. Assume that all heat loss is radiative through the side and top of the pot, given that wood is a relatively poor thermal conductor. The coffee shop ambient temperature T= 20.0 ° C. a) Find the rate at which the coffee losses heat. b) Assuming constant heat loss rate, what is the coffee temperature after 10.0 minutes have elapsed? C.-4.19 x 10' J/kg °C, pn = 1.00 x 10' kg/m', a = 5.67 x 10 W/m K %3D %3D Figure P6 Coffee Pot Table
Expert Solution
Step 1

Given information:

Mass of coffee (m) = 10.0 kg

Initial temperature of the coffee (Tc) = 95 0C = 368 0K

The ambient atmospheric temperature (Ta) = 293 0K

The radius of the pot (r) = 8 cm = 0.08 m

The height of the pot (h) = 50 cm = 0.5 m

The emissivity of the steel surface (e) = 0.600

The Stephen-Boltzmann constant (σ) = 5.67 x 10 -8 W/m2

The rate of heat loss of the coffee is given as:

Qr = eσATc4-Ta4=0.600(5.67×10-8)(πr2+2πrh)(3684-2934)Qr=101.29 J/s or 101.29 W

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