P-V-T SURFACE FOR AN IDEAL GAS

• For a fixed number of molecules/moles The Ideal Gas Law forms the surface of a three-dimensional plot where the axis are Pressure, Volume, and Temperature.
  
  
• Lines of constant pressure, constant volume, and constant temperature form a coordinate system labeling the location of an ideal gas.
  

• Robert Boyle showed that the pressure of a low-density gas is inversely proportional to the volume of a gas when the temperature is held constant, P α 1/V for constant temperature. Blowup of PV diagram for isothermals.
  
  
• Jacques Charles and Gay-Lussac showed that the pressure of a low-density gas is proportional to the temperature of the gas when the volume is held constant, P α T for constant volume.
  
  
• The ideal gas law is only valid for low-density gas. Fortunately, most ordinary gases behave like an ideal gas because the sizes of the molecules are small compared to their separation. None the less, there is still a PVT surface for high-density gases only it is not the ideal equation of state PV = nRT. One such equation is that of the van der Waals equation.

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