What is the relationship between refractive index and pressure in gases?

[Aeon]

Dependence of refractive index on pressure

Homework Statement

Show that, in a gas (for which the refractive index is close to 1), the refractive index depends on the pressure as $$n_r = 1+ K\times p$$, and find the value of K.

Homework Equations

$$n_r = 1+ K\times p$$
Clausius-Mossotti equation: $$\frac{\epsilon_r - 1}{\epsilon_r + 2} = \frac{\rho N_a \alpha}{3M\epsilon_0}$$
$$\alpha^'\ = \frac{\alpha}{4\pi \epsilon_0}$$
$$n_r = \epsilon_r^{1/2}$$

The Attempt at a Solution

Any help to get me started, conceptual or mathematical, will be appreciated!

PS: I think I have posted this question in the right forum now. I had posted it in Advanced Physics before... I would have deleted my other post, but I can't.

 

[ehild]

Which quantity on the right-hand side depends on the pressure p?

ehild

 

[Aeon]

Supposing you're talking about the Clausius equation, I would say $$\frac{\rho}{M} = \frac{1}{V_m}$$ depends on the pressure (inversely to how it behaves in phase diagrams).

 

[Aeon]

The problem confuses me. I don't understand how I can go from the Clausius equation to $$n_r = 1+ K\times p$$

 

[ehild]

Think of the ideal gas law. What is the relation between density and pressure?

ehild

 

[ArthurIhde]

i got confused

 

[Aeon]

$$\rho = \frac{mp}{nRT}$$

To be honest, I'm starting to think I don't even NEED the Clausius equation to solve this problem...

Do I?

 

[ehild]

You do. Check the ideal gas law. It is wrong as you wrote it.
The symbol n in the ideal gas low means number of moles, n= mass/molar mass. And look after the meaning of the symbols in the Clausius equation.

ehild