Help my husband calculate the irradiance of the sun!

[Pretty in Pink]

Can anyone here walk us through this? It's for a meteorology class he's taking and we're both stumped. We are given the surface temp. of the sun, 5780 K, and asked to calculate the irradiance using the Steffan-Boltzmann Law.

 

Please and thank you!!
 

[regentrude]

I do not understand the problem: has he put the temperature simply into the Stefan-Boltzmann Law? It's plug&chug.

 

Or does he not know what S-B-Law is? Google is your best friend:

http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law

 

 

[Pretty in Pink]

No, we have the formula in front of us. We plugged the temp in. We got the wrong answer. Help!

 

Here's the problem:
 

1. The average temperature of the sun is 5780 K. Using the Stefan-Boltzmann Law, calculate the average irradiance of the sun. Show your work and include appropriate units. Hint: Formula- E* = sigmaT^4 ^ is for the power sign. When you input your answer, be sure to use the ^ sign to denote "to the power of". This formula may help you with this problem: E* = sigmaT^4 (Points : 1)

Here's the problem with the temp plugged in:

 

E* = (5.67 x 10^-8 W m^-2 K^-4) (5780 K^4)

 

Our answer is:

 

E* = 3.23 x 10 ^-8 W m ^-2

 

The correct answer, according to the quiz, is:

 

E* = 6.35 x 10^7 W m^–2
 

[regentrude]

Did you raise the TEMPERATURE value to the power of four as well? Your expression

 

 

E* = (5.67 x 10^-8 W m^-2 K^-4) (5780 K^4)

 

has the exponent 4 only on the unit Kelvin, but not on the number 5780.

You need parentheses and it should be (5780K)^4

 

 

ETA: It is obvious that your two equations

 

 

E* = (5.67 x 10^-8 W m^-2 K^-4) (5780 K^4)

Our answer is:

E* = 3.23 x 10 ^-8 W m ^-2

 

have to be inconsistent: if the constant is already 5x10^-8, you can't get LESS when you multiply it by (5780)^4.

You have a math mistake somewhere.

 

[Pretty in Pink]

Okay, let's try this again! :)

 

E* = (5.67 x 10^-8 W m^-2 K^-4)(T^4)   and   T = 5780, so:

 

E* = (5.67 x 10^-8 W m^-2 K^-4)(5780K)^4

 

E* = (5.67 x 10^-8 W m^-2 K^-4)(1.12 x 10^9)(K^4)

 

E* = 6.35 x 10^1 W m^-2

 

Which is almost right, save for the exponent on the 10, which is 7 in the answer on the quiz:

 

E* = 6.35 x 10^7 W m^–2

 

Do you see my mistake?

 

ETA: NM. Our mistake is in the scientific notation on 5780^4. It's 10^15, not 10^9. Our calculator needs to be replaced apparently. :P

 

 

 

 

[Pretty in Pink]

One more question. My husband needs to know why you raise BOTH the 5780 AND the K to the fourth power. Why not only one of them?

[regentrude]

One more question. My husband needs to know why you raise BOTH the 5780 AND the K to the fourth power. Why not only one of them?

 

The quantity raised to the fourth power is the temperature.

The temperature is 5780K. The unit is part of the quantity, as is the number. So T=5780K, and T is raised to the power of four.

All physical quantities have units, and whatever operation is done with it must be done with the entire quantity, number and unit

 

Or is your DH's question why (5780K)^4=5780^4K^4? That is laws of exponents, prealgebra.

It is easy to see if you recall that exponent is shorthand for repeated multiplication:

 (5780K)*(5780K)*(5780K)*(5780K)=5780*5780*5780*5780*K*K*K*K (Commutative property)

[Pretty in Pink]

Thank you. Now he magically understands. I guess I'm not a good enough teacher. :P