**Text:**"Star B is the same size as the Sun. If its temperature is 9 times higher than the Sun's, then the luminosity of Star B is ______ times that of the Sun.(Note that Star B could not be on the main sequence!)"**Explanation:**This statement involves a concept from astrophysics known as the luminosity-temperature relation. For stars of the same size, the luminosity (L) can be related to temperature (T) using the formula:\[ L \propto T^4 \]Since Star B is 9 times hotter than the Sun, you would calculate its luminosity as follows:\[L_{\text{Star B}} = (9)^4 = 6561 \]Therefore, the luminosity of Star B is 6561 times that of the Sun. The phrase "Note that Star B could not be on the main sequence" indicates that such high temperatures and luminosities for stars of this size do not match the typical properties of main sequence stars, which are characterized by a stable phase of hydrogen burning.

Answered: Star B is the same size as the Sun. If…

Applications and Investigations in Earth Science (9th Edition)

9th Edition

ISBN:9780134746241

Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa

Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa

Chapter1: The Study Of Minerals

Section: Chapter Questions

Problem 1LR

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Question

**Text:**

"Star B is the same size as the Sun. If its temperature is 9 times higher than the Sun's, then the luminosity of Star B is ______ times that of the Sun.

(Note that Star B could not be on the main sequence!)"

**Explanation:**

This statement involves a concept from astrophysics known as the luminosity-temperature relation. For stars of the same size, the luminosity (L) can be related to temperature (T) using the formula:

\[
L \propto T^4
\]

Since Star B is 9 times hotter than the Sun, you would calculate its luminosity as follows:

\[
L_{\text{Star B}} = (9)^4 = 6561
\]

Therefore, the luminosity of Star B is 6561 times that of the Sun. The phrase "Note that Star B could not be on the main sequence" indicates that such high temperatures and luminosities for stars of this size do not match the typical properties of main sequence stars, which are characterized by a stable phase of hydrogen burning.

Expert Solution

Step 1

Luminosity is the total energy emitted per second from a star and it depends on the effective temperature(T) and the total surface area of the star. According to Stefan-Boltzmann law of blackbody radiation, the flux or energy emitted per second from each square unit of star's surface is $σ$ T⁴( $σ$ = Stefan-Boltzmann constant) and area is 4 $π$ R²(R= Radius of the star). So, star's luminosity is (Flux $\times$ Area) or 4 $π$ R² $σ$ T⁴.

In simpler words, a star's luminosity is proportional to its effective temperature to the 4^thpower. When two stars are of same size with same radius, the hotter star is more luminous.