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A cubical block of mass 1.0 kg and edge 5.0 cm is heated to 227 deg C and then placed in an evacuated enclosure kept at 27 deg C. Treating the block as a blackbody, find the initial rate of fall of its temperature. Specific heat capacity of the block = 400 J/kg-K. (Take sigma = 5.67e-8 W/m²-K⁴.)

1. 0.09 deg C/s
2. 0.12 deg C/s
3. 0.15 deg C/s
4. 0.18 deg C/s

Correct answer: 0.12 deg C/s

Solution

P = 5.67e-8 * 0.015 * (500⁴ - 300⁴) ~ 46.3 W, and dT/dt = 46.3/(1*400) ~ 0.12 deg C/s.

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