How do I calculate lines of constant pressure in a Brayton cycle diagram?

[ingmarvandijk]

Hey guys (and girls?)

I'm new here, just registered, because I have a problem that my textbooks or google can't help me with:

I am making "Brayton cycle diagrams" for a study in jet engine efficiency. It's basically a Temperature - Entropy diagram for those of you who are unfamiliar with it. I know how to calculate the temperature increase with a pressure increase (basic isentropic relationships), and the entropy increase with fuel addition (delta S = q * LN( delta T)).

The problem I'm having is calculating lines of constant pressure in this diagram. Every source talks about them, but no source tells me how to calculate them. I know they are supposed to be increasing curves (the temperature difference for a pressure ratio is higher at higher entropy).

Does anyone have a clue to calculate these isobars?

Any help is greatly appreciated!

 

[ingmarvandijk]

Some extra insight:

There are 2 important processes.
The first one is compression, where the pressure increases, the temperature as a result, and the entropy remains constant.
The second process is heat addition (or subtraction) where the temperature changes and the entropy follows

Also, in the formula for fuel addition it should of course be LN(T2/T1) instead of Delta T.