Deriving (∂T/∂P)s from T, V, Cp, α, and κT

[mdawg467]

Im trying to understand this concept of deriving an expression for ($\frac{\partial T}{\partial P}$)_s in terms of T, V, C_p, $\alpha$, and $\kappa$_T

($\frac{\partial T}{\partial P}$)_s is evaluated by measuring the temperature change and the specific volume change accompanying a small pressure change in a reversible adiabatic process.

I attached the derivation that the book does, but I cannot follow it. Any help would be greatly appreciated!

Thanks

 

[qbert]

There are a lot of steps in that simple looking derivation. Where are you lost?

 

[Philip Wood]

Don't understand the notation in your thumbnail, but append my derivation, expressed in ordinary partial derivative notation.

 

[mdawg467]

Don't understand the notation in your thumbnail, but append my derivation, expressed in ordinary partial derivative notation.

Thanks dude, I was getting lost with the notation as well. This helps out big time.. Not sure what the book was doing lol.