Luminosity and Surface Area

[Sastronaut]

Homework Statement

A typical adult burns about 2500 Calories in one day.
1)How much energy does the average human emit every second
2)What is another term to use for expressing a “Joule per second”?
3)From your answers to (1) and (2), you just determined the “luminosity” of the average human. If the average body temperature is 98.6℉. What is the area over which a human body emits its energy?
4)Look up the surface area of human skin. How does your result from (3) compare to this value? Why is there a difference?

Homework Equations

The Attempt at a Solution

1. 2500 Calories/day | 4184 Joules/1Calorie | 1day/24hrs | 1hr/60min | 1min/60sec | = 121.06 J/s

2. Watt

3. L=(5.67×〖10〗^(-8) W/(m^2 K^4 ))(A)(T^4 )

121.06W = (5.67x10^-8 W/m^2K^4)(A)(310K)^4 

A= .2312 m^2

4. average adult skin surface area = 1.8 m^2. ****If I did my math correctly...could I please have some opinions on what would create the difference in my answers in part 3 and 4? Thanks PF! I though perhaps it relates to the fact that different parts of the body radiate at different rates?

 

[barryj]

For one thing, remember that when a body radiates energy, it also accepts energy from its environment.
Also, the body may experience cooling from evaporation of water on the skin.

 

[barryj]

Attached is an example from a physics book

 

[Sastronaut]

Thank you very much for your help!

 

[Nickie]

Your calculations for parts 1-3 are correct. The difference in the answers for parts 3 and 4 is due to the fact that the calculation for luminosity assumes that the entire body is emitting energy at the same rate, which is not the case. The surface area of the skin is much larger than the area calculated for the entire body, which means that the energy emitted per unit area is actually lower. This is because different parts of the body have different temperatures and therefore emit energy at different rates. Additionally, not all of the energy produced by the body is emitted as radiation, some is used for other bodily processes such as metabolism. This is why there is a difference in the values calculated for the luminosity and the surface area.