ChemE Thermo- Reading a PH diagram

There are two old-school ways of succinctly communicating state-variables for single-component systems: Tables and Diagrams. For some reason, it's more common to present refrigerant data in a diagram than in a table. This problem-of-the-day goes a little bit in-depth on reading the methane PH diagram in order to solve a simple energy and entropy balance on a compressor. Determination of additional variables is up to you!