How much power is radiated by a tungsten sphere (emissivity, e = 0.35) of radius

Question

How much power is radiated by a tungsten sphere (emissivity, e = 0.35) of radius 19cm at a temperature of 24 degrees C? Express your answer using two significant figures. If the sphere is enclosed in a room whose walls are kept at -5 degrees C, what is the net flow rate of energy out of the sphere? Express your answer using two significant figures.

Explanation / Answer

1. Q = m*c*deltaT = m*c*(Tf - 9.6) => Tf = Q/(m*c) + 9.6 = 7720/(3.0*4200) + 9.6 = 10.2oC 2. P = Q/t where Q = m*c*deltaT...so Q = 0.250kg*4200J/kg-oC*(50-20) = 31500J... So t = Q/P = 31500/349 = 90.3s 3. Key -- Heat out Qiut from the substance = Q into the cup, thermometer & water So Q out = m*c*deltaT = 0.188kg*c*(323-35.3) = 54.1c Q in = m*c*deltaT for each substance = 0.100kg*900J/kg-oC*(35.3-11.5) + 0.166kg*4200*(35.3-11.5) + 0.018*840*(35.3-11.5) = 19165J So 54.1c = 19165 => c = 19165/54.1 = 354J/kg-oC 4. H = A*e*sigma*T^4 = 4*pi*(0.19m)^2*0.35*5.67x10^-8*(273+27)^… = 72.9W Net heat flow = A*e*sigma*(T^4 = Ts^4) = 4*pi*(0.19)^2*.35*5.67x10^-8*(300^4 - 268^4) = 26.5W 5. H = kA*(Th - Tc)/L = 0.8*(2.0*1.5)*(15-(-7))/3.2x10^-3 = 1.65x10^4W

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