Relationship of temperature and radius.

In summary, the conversation discusses the change in temperature and radius of a main sequence star as it becomes a supergiant. The question asks for the radius of the star in terms of solar radii. Both the speaker and their friend use different equations to solve the problem, with the friend using the relationship between temperature and radius to calculate the answer of 250 solar radii. The conversation also briefly touches on the concept of luminosity and its relationship to temperature and radius.
  • #1
darkar
187
0
Here's the question,

Initially, a main sequence star has a surface temperature of 25000 K and a radius 10 times that of the sun. Its temperature drop to 5000 K as it becomes a supergiant. What is its radius in term of solar radii?
a) 25
b) 50
c) 100
d) 250
e) 500

Well, I tried to do it using luminosity , L=4πR²σT⁴. Since the luminosity is not given, i use the Morgan-Keenan spectral classification to get the luminosity of the star at each phase, that's is at temperature of 25000 K has luminosity of 20,000 and for 5000 K has luminosity of 0.4. I got my final answer as 1.18 solar radius, which mean my answer is wrong. How should i approach the problem? and is that the spectral classification is only for main star sequence? and my friend use the relationship of temperature^4 is inversely proportional to 1/(radius)^2 and he got the answer for 250. BUt doesn't that mean that the luminosity is the same, is this true?

Thanks!
 
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  • #2
If the total energy output is considered the same, then one can establish an equivalence, much like your friend did.

r12*T14 = r22*T24

or r1*T12 = r2*T22

or r2 = r1*(T1/T2)2

So what does this say about the luminosities?
 
  • #3
I see... so the luminosities in that two phases are the same.

Thanks!
 

1. How does temperature affect the radius of an object?

The relationship between temperature and radius is known as thermal expansion. When an object is heated, the particles within the object gain energy and move more rapidly, causing the object to expand. This expansion results in an increase in the object's radius.

2. Is there a direct correlation between temperature and radius?

Yes, there is a direct correlation between temperature and radius. As the temperature increases, the radius of an object will also increase due to thermal expansion. Similarly, as the temperature decreases, the radius will decrease due to thermal contraction.

3. How does the material of an object affect the relationship between temperature and radius?

The material of an object can greatly impact the relationship between temperature and radius. Different materials have different coefficients of thermal expansion, which determine how much an object will expand or contract with a change in temperature. Some materials, such as metals, have a higher coefficient of thermal expansion and will expand more with an increase in temperature compared to other materials.

4. Can the relationship between temperature and radius be applied to all objects?

In general, the relationship between temperature and radius can be applied to most solid objects. However, some materials, such as rubber and some plastics, may exhibit a reverse relationship, where they contract with an increase in temperature. Additionally, the relationship may not hold true for objects at extremely high or low temperatures, as other factors may come into play.

5. How does the relationship between temperature and radius impact real world applications?

The relationship between temperature and radius has many practical applications in everyday life. For example, it is important to consider thermal expansion when constructing bridges and buildings, as changes in temperature can affect the stability of these structures. It is also a crucial factor in the design and functioning of various mechanical and electrical systems, such as car engines and electronic devices. In addition, thermal expansion is utilized in industries such as glassmaking and ceramics, where controlled heating and cooling processes are used to create specific shapes and sizes.

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