Over the holidays you want your guests to enjoy a nice hot beverage but you only
ID: 1863198 • Letter: O
Question
Over the holidays you want your guests to enjoy a nice hot beverage but you only have paper cups with plastic lids. Having taken EASC2213, you want to estimate how much faster you loose heat without a lid compared to with a lid or the ratio of the heat transfer for the hot beverage without a lid compared to a hot beverage with a lid. Assuming that the paper cup is at the temperature of the liquid and it is roughly a cylinder, determine the ratio of radiation and convection losses without a lid to the value with a lid.
With the lid on, assume heat is lost through the cylindrical surface only (ie the base and lid are insulated). With the lid off, assume heat is lost through the cylindrical side and top circular area.
Diameter = 13 cm, height = 6 cm, convective coefficient h = 16 W/m2K, emissivity = 0.87,
the beverage temperature = 66 Celcius and the room temperature is 25 Celcius.
Explanation / Answer
WITH LEAD
Q(CONVECTION) =h A (66 - 25)
A=pi (0.13)(0.06)
Q(RADIATION) =(5.67 * 10^-8)(0.87)A(T^4 - t^4)
A=pi(0.13)(0.06)
T=66+273K
t=25+273K
TOTAL Q=Q(CONVECT) + Q(RADIATION)
WITHOUT LEAD
q(CONVECTION) =h A (66 - 25)
A=pi (0.13)(0.06)+ pi(0.13/2)^2
q(RADIATION) =(5.67 * 10^-8)(0.87)A(T^4 - t^4)
A=pi(0.13)(0.06) + pi (0.13/2)^2
T=66+273K
t=25+273K
TOTAL Q =q(CONVECT) + q(RADIATION)
GET WHATEVER U HAVE 2 FIND
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