# Temperature based on colour index using Planck's law

• B
• heavystray
In summary, the person is trying to find the temperature of stars using the B-V magnitude and the Planck law. They are unsure of how to solve for T and have tried but reached a dead end. They ask for help in integrating λ over the bandpass of the filter and the other person suggests using numerical methods and coding in Mathematica, Matlab, or Python. The person responds that they do not know how to use those programs and will solve it using a graph instead.
heavystray
Hi, I'm trying to find temperature of stars using the stars' B-V magnitude by using the Planck law. However i do not know how to solve for T (assume other quantities are all given and determined first). Any idea how to do so? I already tried to do it but reach a dead end. Here I attached the Planck equation. h is Planck's constant, k is boltzman's constant, c is the speed of light,

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It should be a simple matter to solve for T numerically. To do it right, you really should integrate λ over the bandpass of the filter.

phyzguy said:
It should be a simple matter to solve for T numerically. To do it right, you really should integrate λ over the bandpass of the filter.
How do you integrate it tho? It'd be great if you can show step by step on how to do it, thanks for answering.

heavystray said:
How do you integrate it tho? It'd be great if you can show step by step on how to do it, thanks for answering.

I would do that numerically as well. You can write some simple code in Mathematica, Matlab, or Python to do it. Do you know how to use any of those?

phyzguy said:
I would do that numerically as well. You can write some simple code in Mathematica, Matlab, or Python to do it. Do you know how to use any of those?
hmmm no..but i think it's ok for now...i'll just solve it using graph, thanks!

## 1. What is the relationship between temperature and color index?

According to Planck's law, there is a direct relationship between temperature and color index. As the temperature increases, the color index shifts towards the blue end of the spectrum, and as the temperature decreases, the color index shifts towards the red end of the spectrum.

## 2. How does Planck's law explain the relationship between temperature and color index?

Planck's law states that the spectrum of radiation emitted by a blackbody is dependent on its temperature. As the temperature increases, the intensity of shorter wavelength light (blue) increases, while the intensity of longer wavelength light (red) decreases, leading to a shift in the overall color index.

## 3. Can Planck's law be used to accurately determine temperature based on color index?

Yes, Planck's law is a well-established formula that can be used to accurately determine temperature based on color index. However, other factors such as the composition and age of the object emitting the light should also be considered for a more accurate determination.

## 4. Are there any limitations to using Planck's law for temperature determination?

One limitation of using Planck's law is that it assumes the object emitting the light is a perfect blackbody, which may not always be the case. Additionally, the presence of dust or other materials in the object's atmosphere can also affect the observed color index and thus the accuracy of the temperature determination.

## 5. What are some real-world applications of using Planck's law for temperature determination?

Planck's law has a wide range of applications, including in astronomy for determining the surface temperatures of stars and planets, in remote sensing for measuring the temperature of objects from a distance, and in materials science for studying the thermal properties of various materials.

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