Final answer:
The percentage increase in total power of blackbody radiation due to a temperature rise from 98.6°F to 103°F can be calculated using the ratio of powers derived from the Stefan-Boltzmann law.
Step-by-step explanation:
To calculate the percentage increase in the total power of radiation when a human body, treated as a blackbody, has its temperature increased from 98.6°F to 103°F, we use Stefan-Boltzmann law. First, convert Fahrenheit to Kelvin (K=T(°F) + 459.67)*5/9, which gives us T1=310.15 K and T2=312.039 K. The Stefan-Boltzmann law is given by P(T) = εσAT^4, where ε is the emissivity, σ is the Stefan-Boltzmann constant, A is the surface area, and T is the absolute temperature in kelvins.
We can simplify the problem by considering the ratio of powers:
Percentage Increase = ((P(T2) - P(T1)) / P(T1)) * 100%
Since ε, σ, and A are constants and will cancel out, we only need the temperatures:
Percentage Increase = ((T2^4 - T1^4) / T1^4) * 100%
Insert the values and calculate the percentage increase.