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Question

A cubical block of mass 1.0  kg and edge 5.0 cm is heated to 227^0 C. It is kept in an evacuated chamber maintained at 27^0 C. Assuming that the block emits radiation like a blackbody, find the rate at which the temperature of the block will decrease. Specific heat capacity of the material of the block is 400 J kg1K1


Solution

Since the cube can be assumend as black body 

e = 1, σ=6.0×108W/m2K4

A = 6×25×104m2

m = 1 kg, S = 400 J/kg - K

T1=227C = 500 K

T2=27C = 300 K.

ms=dθdt=Aσe(T41T42)

dθdt

1×6×108×6×25×104[(500)4(300)4]1×400

= 36×25×544400×104

= 1224 ×104

= 0.12240C/s

= 0.120C/s

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