Help with radiant intensity, spectral intensity, etc....

[drod31]

Hello Everybody,

I'm having issues defining a set of equations that calculates the Temperature of a black body object when provided with one of the following:

• Radiant Intensity [W sr-1]
• Spectral Intensity [W sr-1 m-1]
  
• Radiance [W sr-1 m-2]
• Spectral Radiance [W sr-1 m-3]
• Irradiance Flux Density [W m-2]
• Spectral Irradiance [W / m-3]

To provide further insight into why I'm looking for this:

The goals is to define a temperature profile of a rocket during its trajectory. If I assume the detector is far enough that the rocket can be considered a point source how can I find the temp profile when given intensities/radiance/etc. at each time step?

Also worth mentioning... at the moment I'm not accounting for atmospheric changes.

I can get the temperature pretty easy when the spectral irradiance is provided (based on online literature).

Any sources that provide examples would be great!

Thanks!

 

[eljose79]

Thank you for sharing your question with the scientific community. Calculating the temperature of a black body object can be a complex task, but I will do my best to provide some guidance and sources for further information.

Firstly, it is important to note that the temperature of a black body object is directly related to its radiance, which is the amount of electromagnetic radiation emitted from the object in a given direction. This means that by knowing the radiance, we can calculate the temperature of the object.

To begin, let's define some terms and equations that will be useful in your calculations:

1. Stefan-Boltzmann Law: This law states that the total radiant emittance of a black body is proportional to the fourth power of its absolute temperature. It can be expressed as:

E = σT^4

Where E is the total radiant emittance, σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W m^-2 K^-4), and T is the absolute temperature.

2. Planck's Law: This law describes the spectral radiance of a black body at a given wavelength and temperature. It can be expressed as:

B(λ,T) = (2hc^2/λ^5) x (1/(e^(hc/λkT) - 1))

Where B(λ,T) is the spectral radiance, h is the Planck constant (6.626 x 10^-34 J s), c is the speed of light (3.00 x 10^8 m/s), λ is the wavelength, k is the Boltzmann constant (1.38 x 10^-23 J/K), and T is the absolute temperature.

3. Wien's Displacement Law: This law states that the peak wavelength of the spectral radiance of a black body is inversely proportional to its temperature. It can be expressed as:

λmax = b/T

Where λmax is the peak wavelength, b is Wien's displacement constant (2.90 x 10^-3 m K), and T is the absolute temperature.

Now, to answer your specific question, we can use the equations above to calculate the temperature of a black body object when provided with different types of intensity or radiance data.

1. Radiant Intensity [W sr-1]: This is the total amount of radiant energy emitted by the object in a given direction. To calculate the temperature, we