The equation 4 you found did not match the P-T curve in the previous post.
I would suggest you find P-T curve, and draw new curves for carnot cycle (usually it was dwan on P-V diagram).
The two constant temperature curves will become two vertical lines in P-T curve.
With ideal gas law: ,
the adiabatic curve (constant can be reduced to
Draw starting point with your initial condition: , then follow the above new PT curve before it touch the PT condensation curve.