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.