what is the difference between pressure-volume and pressure-specific volume curves? since volume is an extensive property why do we plot pressure and volume curves for different processes?
Generally you can graph a process using any two independent thermodynamic variables. Which ones you choose depends on what you want to analyze or show. For example, if you want to analyze work, you generally use a pressure volume graph. You can use other thermodynamic variables, but pressure and volume are directly measurable (with instruments) whereas other thermodynamic variables may not be (e.g., entropy and internal energy). For a closed system boundary work done by a process is the area under the PV curve. The net work done in a thermodynamic cycle would be the area enclosed by the PV cycle, and so forth.
Insofar as using specific volume $v$ or total volume $V$ is concerned, you can use either. However, for a closed system the mass is constant (e.g., ideal gas in cylinder/piston). Since the mass is fixed (and can be obtained by ideal gas law), you normally use total volume $V$ to find total work done by/on the mass. For open systems where the mass flow rate may be a variable, you would use the specific volume (volume per unit mass) to compute the work done per unit mass. Multiplying the work done per unit mass that by the mass flow rate will give you the rate of doing work (power).
Hope this helps.