Python Max Distance from which a python detects infrared radiation

[Venerable R]

Homework Statement

A python can detect thermal radiation with intensity greater than .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.

I = .60 W/m²
e = 0.97
T = 303 K
A = 1.8 m²
d = ? (m)

Homework Equations

[/B]
λ = (2.9*10⁶ nm⋅K)/ Temp (in K)
I = P/(4πr²)
Q/Δt = eσAT⁴
σ = 5.67 * 10 ^-8 W/(m²⋅K⁴)

The Attempt at a Solution

λ = (2.9*10⁶ nm⋅K)/ 303 K = 9571 nm

And if P = Watts, A = m², and I = W/m²
Then, P = I*A → .60*1.8 = 1.08 W

.60 W/m² = (0.97 * 1.08 W)/(4πr²)
r = .37 m

Honestly, I'm not sure what else to do. I don't think "P" is correct.

 

[BvU]

Hello R, welcome to PF :)

I agree P probably isn't correct. Is it clear what the relevant equations you are listing stand for ?
I like the third one: Q/time (aka P !), according to the Stefan-Boltzmann law
You have all the ingredients to evaluate the human body emission $P_{emit}$. It's rather a lot.
Your first equation tells you the peak wavelength of the intensity distribution spectrum is at over 9000 nm, so most of this P is in the infrared.
I suppose (but don't know for sure -- perhaps someone else can confirm or correct) that fraction is precisely the emissivity factor.

And that is the P you want to distribute over a sphere using your second equation. By the time r is so big that I < 0.6 W/m² you've found the range.

 

[Venerable R]

Hello R, welcome to PF :)

I agree P probably isn't correct. Is it clear what the relevant equations you are listing stand for ?
I like the third one: Q/time (aka P !), according to the Stefan-Boltzmann law
You have all the ingredients to evaluate the human body emission $P_{emit}$. It's rather a lot.
Your first equation tells you the peak wavelength of the intensity distribution spectrum is at over 9000 nm, so most of this P is in the infrared.
I suppose (but don't know for sure -- perhaps someone else can confirm or correct) that fraction is precisely the emissivity factor.

And that is the P you want to distribute over a sphere using your second equation. By the time r is so big that I < 0.6 W/m² you've found the range.

Oh! So, using P = eσAT⁴, I found P = 834 W.
Then, I = P/(4πr²), I found that r = 10.5 m!

That's seems realistic! Thank you for all your help! :D

 

[BvU]

I hope it's the right answer...
Tried to check by working it out for a mouse (after all, a much more likely item on the snake menu) of, say, 25 gram, so 1/3500 times the weight and some (1/3500)^2/3 the area. About 66 cm, so life isn't all that easy for a snake...

I also think I remember hearing that snakes only 'see' movement.

Oh, well, with physics you can't know everything (although some physicists seem to think otherwise ;) )