Phase Diagrams of Pure Substances:
a Tutorial





The Pressure-Volume-
Temperature Relation


Animation of the Piston-Cylinder


Generating the Tv diagram


Details of the Tv diagram


PvT Surface with Solid Region


Projections of the PvT Surface


The PT Projection




Quiz on the PT Diagram


Quiz on the Tv Diagram


Quiz on General Topics




This tutorial was written in 2000 to fulfill part of the requirements of a University of South Florida Instructional Development grant. Over the years, it has received positive feedback from folks who have stumbled onto it on the web. I hope you find it useful.


In thermodynamics, a system is a region of space of which we have some interest.  Often the system will consist of one or several pieces of equipment that we wish to use to accomplish a particular task.  It may be a boiler that we want to use to make steam, a pump to circulate water, or a gas turbine to produce power.  Most thermodynamics problems involve finding the heat and work flows that must be supplied to (or removed from) the system to obtain the desired result.

In your study of thermodynamics, you will find that these heat and work flows depend on the properties of the material inside or flowing through the system.  For instance, if you want to change the temperature of one pound of water by 10 degrees, the heat required will be different from that needed to change the temperature of one pound of air by 10 degrees. 

Thus, before you learn how to apply the laws of thermodynamics to solve for heat and work flows, you must first understand a bit about properties of materials.

The purpose of this tutorial is to familiarize the reader with the relationship between three important properties of pure substances: pressure, specific volume, and temperature.   The relationship between these properties generally is given in the form of a phase diagram, in which the different regions of phase state (solid, liquid, and vapor and their combinations) are shown.  An understanding of such diagrams is essential to thermodynamics because there will be many occasions in which you will have to refer to a phase diagram (or a tabular representation of one) in order to obtain needed property information.


Specifically, at the end of this tutorial the reader will

  • understand the different types of properties (intensive, extensive, specific) used to characterize pure substances and know how many of them can be regarded as independent.

  • be able to identify the various parts of a three dimension Pressure-Volume-Temperature (PvT) phase diagram including those regions where a single phase exists and those where two phases coexist.

  • understand the various two-dimensional projections of the three-dimensional PvT surface.

  • know all of the basic nomenclature associated with phase diagrams of pure substances.


Later tutorials will focus on using phase diagrams to obtain property information, not only about temperature, pressure and specific volume but for other properties as well.

This tutorial can be followed from one page to the next or you can jump to different topics using the Contents.   The latter is recommended only if you have already been through the tutorial once.

Before we jump into the relation between pressure, specific volume and temperature, we need to discuss a few general points about thermodynamic properties.   This is done on the next page.


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