Chapter 12, Problem 1QAP

To determine

Whether the statement is true or false.

Answer to Problem 1QAP

The statement is false.

Explanation of Solution

Mass–luminosity relationship is an equation that shows the relation between mass and luminosity of star. It shows that mass is directly proportional to luminosity. It also gives graphical representation with mass on x-axis and luminosity on y-axis.

Write the expression for Mass–luminosity relationship.

$\left(\frac{L}{L_{\odot }}\right)={\left(\frac{M}{M_{\odot }}\right)}^{3.5}$

Here, $L$ is the luminosity of star, $L_{\odot }$ is the luminosity of Sun, $M$ is the mass of star and $M_{\odot }$ is the mass of star.

This equation only applies to main-sequence stars with masses $2M_{\odot }<M<55M_{\odot }$. It does not apply on red giant or white dwarf stars.

Conclusion:

The luminosity of star would increase about $11\text{times}$ if its mass is increased by two times. Thus, the statement is false.