# Estimation of central temperature of a star

1. Feb 22, 2012

### Darkkk

Problem:

Relatively low mass stars can be shown to have their radii dependent on their mass as;

R$\propto$M1/2

From this, show that the temperature in kelvin at the centre of such a star can be estimated to be

$\approx$24$\times$106(M/Msolar)1/2

Relevant Equations:

Tc=(2/3ℝ)$\times$Pc$\times$(R3/M)

Attempt at a Solution:

I tried to sub in the relation between R and M of the star, but to be quite honest I didn't see myself getting very far...Any pointers at all would be much appreciated! Not too sure on this one.

2. Feb 23, 2012

### zhermes

What did you get when you plugged in?
Do you know $P_c$ and $\mathcal{R}$

3. Feb 24, 2012

### Darkkk

I do know R=8.314 joules per Kelvin but Pc is unknown, Im assuming the proportion relation will be used at the end of the problem to get the temperature in terms of the solar mass. Im just not quite sure what the first step is. Perhaps I ought to sub the Tc given in the question into the central pressure equation Pc. What do you think? sounds like circular logic to me...

4. Feb 24, 2012

### zhermes

The first step is to plug in the mass-radius relation. That way you eliminate the radius from the equation. You know R, so all you need to find is the central pressure to solve for the temperature.

5. Feb 25, 2012

### Darkkk

Ah yes I see! I have it now. Thank you for the advice :)