Max Distance from which a python detects infrared radiation

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Discussion Overview

The discussion revolves around calculating the maximum distance from which a python can detect infrared radiation emitted by a human body, modeled as a point source. The context includes theoretical and mathematical reasoning related to thermal radiation detection.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Exploratory

Main Points Raised

  • Post 1 presents the problem statement and initial calculations, questioning the correctness of the power (P) value used.
  • Post 2 agrees with the uncertainty regarding P and discusses the relevance of the equations listed, particularly the Stefan-Boltzmann law for calculating emitted power.
  • Post 2 also suggests that the peak wavelength of the emitted radiation is in the infrared range and speculates on the role of emissivity in determining the power distribution.
  • Post 3 calculates the emitted power (P) as 834 W and subsequently finds a maximum detection range of 10.5 m, expressing satisfaction with the result.
  • Post 4 explores a related scenario involving a mouse, estimating a detection range of about 66 cm, and mentions that snakes may primarily detect movement rather than static heat sources.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the calculations and the interpretation of the equations. There is no consensus on the correctness of the initial power value or the implications of the results, as different scenarios are explored without a definitive conclusion.

Contextual Notes

Participants note potential limitations in the assumptions made regarding the human body as a point source and the applicability of the calculations to different animals, such as mice. The discussion also highlights the complexity of thermal detection in snakes.

Venerable R
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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.
 
Last edited:
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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.
 
BvU said:
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
 
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 ;) )