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A black body at 227°C radiates heat at the rate of 7 cal/cm²·s. At a temperature of 727°C, the rate of heat radiated in the same units will be:

1. 50
2. 112
3. 80
4. 60

Correct answer: 112

Solution

The rate of heat radiation is proportional to the fourth power of the absolute temperature (Stefan-Boltzmann law). Converting temperatures to Kelvin: T1 = 227 + 273 = 500 K, T2 = 727 + 273 = 1000 K. Using the ratio (R2/R1) = (T2/T1)^4, we get R2 = 7 × (1000/500)^4 = 7 × 16 = 112 cal/cm²·s.

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