Finding a relationship using 1st Law of Thermodynamics

[Charanjit]

1. Homework Statement

Derive a relationship between dq/T , dT/T, dp/p , Cp , and R for an ideal gas.

2. Homework Equations

dQ = dU + dW and/or dq = du + dw (for a unit mass)
p*d(alpha) = dw (alpha = specific volume V/m)
du = Cv*dT
p(alpha) = RT (Ideal gas equation, a different form)
Cv + R = Cp


3. The Attempt at a Solution

I went through the derivation and got the following:

dq = Cp*dT - R*T*dp/p

I have no clue what to do from here. Any help? Or is this correct?

 

[Charanjit]

After posting this, I found something, why not divide both sides by T, that will give us the relationship the question wanted right?