Question

A python can detect thermal radiation with intensity greater than 0.60 W/m2. A typical human body has a surface area of 1.8 m2, a surface temperature of 30∘C, and an emissivity e = 0.97 at infrared wavelengths.

What is the maximum distance from which a python can detect your presence? You can model the human body as a point source of radiation.

Answer 1

$$ P=e \sigma A T^{4} $$

where:

$$ \begin{aligned} &\sigma=\frac{2 \pi^{5} k^{4}}{15 c^{2} h^{3}}=5.670373 \times 10^{-8} \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-4} \\ &A=1.8 \mathrm{~m}^{2} \\ &e=0.97 \\ &T=30^{\circ} \mathrm{C}+273 \mathrm{~K}=303 \mathrm{~K} \end{aligned} $$

so:

$$ P=834.5 \mathrm{~W} $$

therefore:

$$ I=\frac{P}{\left(4 \pi r^{2}\right)} \rightarrow r=\sqrt{\frac{P}{(4 \pi I)}}=\sqrt{\frac{834.5 W}{4 \pi\left(0.6 W \cdot m^{-2}\right)}}=10.52 \mathrm{~m} $$