Rate of heat radiated from a person

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Homework Help Overview

The discussion revolves around calculating the percentage increase in the rate of heat radiated from a person based on changes in skin temperature, using Stefan's Law of emission.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the application of Stefan's Law to determine the percentage increase in heat radiation. There is a focus on correctly interpreting the results as a percentage rather than a ratio.

Discussion Status

Some participants have provided guidance on the correct interpretation of the calculations, noting the need to convert a ratio into a percentage. There is a general agreement on the revised calculation method, though no explicit consensus on the final answer has been reached.

Contextual Notes

Participants are discussing the implications of temperature changes on heat radiation, with attention to the correct mathematical representation of their findings. The original poster's initial calculation was noted to be incorrect in terms of its representation as a percentage.

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Homework Statement


What is the percentage increase in the rate of heat radiated from a person with a surface skin temperature of 34.0 °C compared with the same person with a skin temperature of 33 °C?


Homework Equations


Stefan's Law of emission:
P = σAeT^4

- P = rate of energy transfer (Watts)
- σ = 5.6696 x 10^–8 W m^–2 K^–4
- A = surface area of the object
- e = emissivity (varies from 0 to 1)
- T = temperature (Kelvins)

The Attempt at a Solution



(34+273)^4/(33+273)^4
= 1.013 % (3sf)

Actual answer is 1.31%
 
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Hendrick said:
(34+273)^4/(33+273)^4
= 1.013 % (3sf)
That isn't a percentage, that's a ratio. You need to multiply by 100 to obtain a percentage.
 
Hootenanny said:
That isn't a percentage, that's a ratio. You need to multiply by 100 to obtain a percentage.

Oh, thanks lol.


Is this right:-

(34+273)^4/(33+273)^4 * 100
= 101.3136113 %

the increase being:
= 101.3136113 % - 100
= 1.3136113%
 
Looks good to me :approve:
 

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