P-V Diagram — All Four Processes

V P ($P_{1}$,$V_{1}$) Isothermal PV = const Adiabatic PV^γ = const Isochoric V = const W = 0 Isobaric P = const ($P_{2}$,$V_{2}$) isothermal Adiabatic steeper than Isothermal Area under curve = Work done by gas Isothermal Adiabatic Isochoric Isobaric γ > 1 → adiabatic steeper

Reading the diagram:

• The isochoric process is a vertical line (V fixed, P changes).
• The isobaric process is a horizontal line (P fixed, V changes).
• The isothermal is a rectangular hyperbola (PV = const).
• The adiabatic is a steeper hyperbola through the same starting point (PV^γ = const, γ > 1).
• The work done by the gas in any process = area enclosed between the curve and the V-axis.