A large square blackbody radiating surface is divided into a grid of equal small

Question

A large square blackbody radiating surface is divided into a grid of equal smaller squares, addressed by integer row and column indices i and j, where -2 i, j 2 . Suppose each grid square has temperature (in kelvins) 300 + i + j. By direct calculation, find at what uniform temperature the entire large square would radiate the same total power as does the actual nonuniform grid. (Keep plenty of significant figures in your calculation.) By how much does this temperature differ from the actual areal mean temperature of the grid? Compare this difference to the estimate derived in class as a correction for the effect of nonuniformity.

Explanation / Answer

there are total 25 grids.

blackbody radiation power is given by sigma*area*temperature^4

where sigma=steffen's constant

if area of complete grid is A, area of each small block is A/25.

so calculating temperature at each grid, taking its 4th power and adding them up,we get

power radiated=sigma*(A/25)*2.02554*10^11

so if uniform temperature required is T,

then sigma*A*T^4=sigma*(A/25)*2.02554*10^11

==>T=300.019998 kelvin

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