How to Derive the Third Equation for Different Values of Gamma?

[orochimaru]

Homework Statement

For the case of a strong shock propagating into a gas with $$\gamma=7/5$$ What is the ratio $$\rho2/\rho1$$

Homework Equations

$$\rho\ u=constant$$

$$P+ \rho\ u^2=constant$$

$$\frac{1}{2} u+ \frac{\gamma }{\gamma -1}\frac{\ P}{\rho} = constant$$

The Attempt at a Solution

I can use the 3 equations in this form to get $$\rho2/\rho1=6$$ but my problem is how do I arrive at the 3rd equation in the given form

we were given equation 3 in the form $$\frac{1}{2} u+ \frac{5}{2}\frac{\ P}{\rho} = constant$$ but this is only valid for $$\gamma=\frac{5}{3}$$

I would like some advice on how to prove the adaption of equation 3 for different values of $$\gamma$$

 

[astrorob]

Hi oro,

Apologies but I don't quite understand what you're question is. If you wanted to solve the Rankine-Hugoniot condition for energy flow for something other than a monatomic gas, what's the problem with just plugging in a different value of $$\gamma$$ into equation 3 in your list?