question archive Theory: Luminosity=4⋅π⋅σ⋅R2⋅T4 where R is the radius of the star, T=temperature, σ=a constant
Theory: Luminosity=4⋅π⋅σ⋅R2⋅T4 where R is the radius of the star, T=temperature, σ=a constant
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Theory: Luminosity=4⋅π⋅σ⋅R2⋅T4 where R is the radius of the star, T=temperature, σ=a constant.
What is the temperature of a star whose luminosity is 1,000⋅LSun and whose radius is 10⋅RSun
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Answer:
The temperature of a star is about 1.78 ?TSun?? or 10,324 K
Step-by-step explanation
From the question we get information
The luminosity of a star ?(L)=1,000LSun??
The radius of a star ?(R)=10RSun??
The temperature of a star ?(T)? is
?LSun?L?=4πσRSun2?TSun4?4πσR2T4??
?LSun?L?=RSun2?TSun4?R2T4??
?T=4(LSun?L?)(R2RSun2??)TSun4???
?T=4(LSun?1,000LSun??)((10RSun?)2RSun2??)TSun4???
?T≈? 1.78 ?TSun??
We know the Sun's temperature ?(TSun?≈? 5,800 K), thus
?T≈1.78(5,800K)?
?T≈? 10,324 K
