A child has a temperature of 101◦F.
If her total skin area is 13 m2, find the en-
ergy loss per second due to radiation, assum-
ing the emissivity is 1. The Stefan-Boltzmann
The energy loss per second due to radiation can be calculated using the Stefan-Boltzmann Law. The Stefan-Boltzmann Law states that the rate at which an object radiates energy is proportional to the fourth power of its temperature. Mathematically, it can be represented as:
E = εσAΔT⁴
Where:
E is the energy loss per second,
ε is the emissivity (given as 1 in this case),
σ is the Stefan-Boltzmann constant (approximately 5.67 × 10⁻⁸ W/(m²K⁴)),
A is the total skin area (given as 13 m²),
ΔT is the temperature difference with respect to the surroundings (in this case, the body's temperature of 101°F should be converted to Kelvin unit).
To calculate the energy loss per second due to radiation, we need to convert the temperature from Fahrenheit to Kelvin:
T(K) = (T(°F) - 32) * (5/9) + 273.15
Let's perform the calculations:
T(K) = (101 - 32) * (5/9) + 273.15
T(K) ≈ 310.93 K
Now, substitute the values into the formula:
E = (1) * (5.67 × 10⁻⁸) * (13) * (310.93 - 273.15)⁴
Calculating this expression will give us the energy loss per second due to radiation.