Exploring the Proportionality of Luminosity & Mass in Stars

[Johnboy]

Homework Statement

Homework Equations

L = M^3.5

The Attempt at a Solution

Am I right in saying that this is the correct proportionality for luminosity and mass in a star?

If it is, i am confused. In an example I have it states that when mass is doubled the luminosity isincreased by a factor of 11 (i.e. 2^3.5). In a question i have the star is 300000 times more luminous than the sun but only 24 times the mass. If I put 24 into this equation, I get 67723, considerably less than 300,000. In another question, the star is 20 times as massive and 10000 times as luminous, this doesn't add up either.

Can someone please tell me where I am going wrong here as this is driving me insane!

 

[gneill]

Homework Statement

Homework Equations

L = M^3.5

The Attempt at a Solution

Am I right in saying that this is the correct proportionality for luminosity and mass in a star?

If it is, i am confused. In an example I have it states that when mass is doubled the luminosity isincreased by a factor of 11 (i.e. 2^3.5). In a question i have the star is 300000 times more luminous than the sun but only 24 times the mass. If I put 24 into this equation, I get 67723, considerably less than 300,000. In another question, the star is 20 times as massive and 10000 times as luminous, this doesn't add up either.

Can someone please tell me where I am going wrong here as this is driving me insane!

The relationship varies slightly depending upon the mass range of the star.

See, for example:

http://en.wikipedia.org/wiki/Mass–luminosity_relation

 

[Johnboy]

Thank you for directing me to that page, where i noticed that the relationship does not apply with red giants.