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?