Spectral radiant exitance when given temperature

• Landshark
In summary, the task is to calculate the spectral radiant exitance for a 10um black body at different temperatures (-12.0°C, 0°C, 12°C, 1600 K, and 2500 K) using Planck's equation. This equation is represented as Mλ = C1 / (λ5 [e(C2/λT) - 1), where λ is the wavelength in micrometres and T is the temperature in Kelvin. C1 and C2 are Planck's constants, and the "e" represents the mathematical constant 2.71828. To solve this equation, one would plug in the given values for λ and T for each temperature and solve for Mλ.
Landshark

Homework Statement

Calculate the spectral radiant exitance for a 10um black body at the following temperatures: -12.0°C, 0°C, 12°C, 1600 K, and 2500 K

Known:
wavelength = 10um
temperature = see above

Homework Equations

Planck's equation I think

The Attempt at a Solution

No idea. I can't figure out the equation (I am a major noob at this). The given equation is:

Mλ = C1 / (λ5 [e(C2/λT) - 1)

λ = wavelength in micrometres
T = temperature in Kelvin

C1 and C2 are supposed to be Planck's constants. What does the "e" mean?

Landshark said:

Homework Statement

Calculate the spectral radiant exitance for a 10um black body at the following temperatures: -12.0°C, 0°C, 12°C, 1600 K, and 2500 K

Known:
wavelength = 10um
temperature = see above

Homework Equations

Planck's equation I think

The Attempt at a Solution

No idea. I can't figure out the equation (I am a major noob at this). The given equation is:

Mλ = C1 / (λ5 [e(C2/λT) - 1)

λ = wavelength in micrometres
T = temperature in Kelvin

C1 and C2 are supposed to be Planck's constants. What does the "e" mean?

WOW, okay, you are missing some fundamental math background here. Have you had a course in calculus yet?

http://en.wikipedia.org/wiki/E_(mathematical_constant)
http://en.wikipedia.org/wiki/Exponential_function

cepheid said:
Have you had a course in calculus yet?

Nope, lol. It's for a geography class.

I assume the e means 2.71828 then?

Last edited by a moderator:
Landshark said:
Nope, lol. It's for a geography class.

I assume the e means 2.71828 then?

Yeah. Did you read those articles (or at least the intros for each one)? The Planck function includes an exponential function (which is e to the power of some variable).

I read the intros, yes. I think I just need an example of this equation done for me. The teacher of my class didn't really give us one.

Related to Spectral radiant exitance when given temperature

Spectral radiant exitance, also known as spectral radiance, is a measure of the amount of electromagnetic radiation emitted from a surface at a specific wavelength and given temperature. It is expressed in watts per square meter per micron (W/m2/μm).

How is spectral radiant exitance calculated?

Spectral radiant exitance is calculated by multiplying the emissivity of the surface by the Stefan-Boltzmann constant (5.67 x 10-8 W/m2/K4) and the fourth power of the temperature in Kelvin.

What is the relationship between temperature and spectral radiant exitance?

As temperature increases, the spectral radiant exitance also increases. This is because the amount of electromagnetic radiation emitted by a surface is directly proportional to its temperature.

What factors can affect the spectral radiant exitance of a surface?

The spectral radiant exitance of a surface can be affected by factors such as the surface temperature, the emissivity of the surface, and the wavelength of the radiation being emitted. Other factors such as the surface composition and geometry can also impact the spectral radiant exitance.

Why is spectral radiant exitance important in scientific research?

Spectral radiant exitance is an important measurement in scientific research as it allows us to understand how much electromagnetic radiation is being emitted from a surface at a specific temperature and wavelength. This can provide valuable insights into the behavior of materials and help in the development of new technologies such as thermal imaging and remote sensing.

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