Question

Assume that the total surface area of a human body is 1.6 m2 and that it radiates like an ideal radiator. Calculate the amount of energy radiated per second by the body if the body temperature is 37°C. Stefan constant σ is 6.0 × 10−8 W m−2 K−4.

Answer 1

The amount of energy radiated per second by the body if the body temperature is 37°C is about 886.58016 J .

Explanation:

Stefan- Boltzmann law states that total energy radiated per unit surface area of a black body across all wavelengths per unit joules is directly related to the fourth power of the black body’s thermodynamic temperature.

According to Stefan- Boltzmann law

$a=\sigma \Sigma T^{2} A$ Joules

Q= Energy radiated/second

σ = Stefan Constant = $6.0 \times 10-8 \mathrm{W} \mathrm{m}-2 \mathrm{K}-4$

T= Absolute Temperature = 273 + 37= 310 ( Given )

Σ= 1 for ideal radiator

A = Area = 1.6 $m^2$

$Q=\sigma \Sigma T^{4} A$

$Q=6.0 \times 10-8 \times 1 \times 1.6 \times(310)^{4}$

$Q=6.0 \times 10-8 \times 1 \times 1.6 \times(3.10 \times 100)^{4}$

$Q=6.0 \times 10-8 \times 1 \times 1.6 \times(3.10)^{4} 10^{8}$

$Q=6.0 \times 1 \times 1.6 \times(3.10 \times 3.10 \times 3.10 \times 3.10)$

$\mathrm{Q}=886.58016 \text { Joules }$

Answer 2

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At 37° celcius the temperature should be

886.58061 joule