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: PV=nRT,
the adiabatic curve PV^\gamma=C (constant can be reduced to P (\frac{nPT}{P})^\gamma=C
or P=C' T^{\gamma/(\gamma-1)}
Draw starting point with your initial condition: P_i,T_i, then follow the above new PT curve before it touch the PT condensation curve.