Physics · Heat transfer: conduction, convection and radiation
If the temperature of a Black body increases by then amount of radiation emmitte
If the temperature of a Black body increases by \( 50 \% \) then amount of radiation emmitted by it in a given time interval will
- A. Increase by \( 800 \% \)
- B. Increase by 400\%
- C. Increase by 200\%
- D. Increase by 1600\%
Step-by-step solution
According to the Stefan-Boltzmann law, the power radiated by a black body is proportional to the fourth power of its absolute temperature, P ∝ T⁴. A 50% increase in temperature means T' = 1.5T. Thus, P' ∝ (1.5T)⁴ = 5.0625 T⁴, so the radiated power increases by a factor of about 5.0625, which corresponds to an increase of approximately 406.25%. Among the given options, the closest is a 400% increase.
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