How many days does it take for a perfect blackbody cube (0.017 m on a side, at 60.0°C) to radiate the same amo?
How many days does it take for a perfect blackbody cube (0.017 m on a side, at 60.0°C) to radiate the same amount of energy that a 100 W lightbulb uses in one hour?
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Verified answer
The Stefan-Boltzmann blackbody law relates intensity to temperature.
E = emissivity = 1
Stefan constant σ = 5.67040E-8 w/m^2-K^4
I = σET^4 = 698.51054 w/m^2
P = I*area = 698.51054*6*0.017^2 = 1.2112172 w
E(bulb) = 360000 J
t = E(bulb)/P = 297221.65 s = 3.4400654 days
The amount of energy the bulb radiates
= Power * Time
= 100 * 3600(sec)
= 360000 Joules.
Now we apply Stefan's law for this perfect blackbody cube.
It has six surfaces each of equal area = 0.017^2 = 0.000289 m^2.
E = 6 * (sigma) * T^4
Sigma is the emissivity of the object. For a perfect black body, it is 1.
So E = 6 * T^4 (6 because there are 6 areas which radiate energy)
Convert 60 degrees to Kelvin => 273 + 60 = 333 K (as Kelvin is the SI unit of temperature)
E = 6 * (333)^4 = 73778221926 Joules of energy/per area/per second..pretty big huh?
Now total energy = 73778221926 * 0.0000289 * 36000 = 76758862091.8 Joules
Time taken in seconds = 76758862091.8/36000 = 2132190.6 seconds = 35536.5 hours = 1480 days approx
Perfect Black Body
Its arguable and there are actually several answers to the question...