Question

A python can detect thermal radiation from objects that differ in temperature from their environment as long as the received intensity of thermal radiation is greater than 0.60 W/m². Your body emits a good deal of thermal radiation; 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. As we've seen, the intensity of a source of radiation decreases with the distance from the source.

If you are outside on a cool, dark night, what is the maximum distance from which a python could detect your presence?

Answer 1

10.52 m

Step-by-step explanation:

The power radiated by a body is given by

P = σεAT⁴ where ε = emissivity = 0.97, T = temperature = 30 C + 273 = 303 K, A = surface area of human body = 1.8 m², σ = 5.67 × 10⁻⁴ W/m²K⁴

P = σεAT⁴ = 5.67 × 10⁻⁸ W/m²K⁴ × 0.97 × 1.8 m² × (303)⁴ = 834.45 W

This is the power radiated by the human body.

The intensity I = P/A where A = 4πr² where r = distance from human body.

I = P/4πr²

r = (√P/πI)/2

If the python is able to detect an intensity of 0.60 W/m², with a power of 834.45 W emitted by the human body, the maximum distance r, is thus

r = (√P/πI)/2 = (√834.45/0.60π)/2 = 21.04/2 = 10.52 m

So, the maximum distance at which a python could detect your presence is 10.52 m.