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Thermodynamics: T-v and P-v Diagrams

T-v and P-v diagrams are used to relate the temperature or the pressure to a change in a substance's specific volume. Refer to the figures below to view a T-v diagram and a P-v diagram.

T-v diagram
P-v diagram

Notice on these diagrams there is a curve. This curve is used to show where the phase change would occur at a constant pressure for the T-v diagram and a constant temperature for the P-v diagram. On both these diagrams there is a peak of the phase change curve called the critical point. At the critical point the liquid will instantly change to a gas. For the T-v diagram the critical point represents the critical pressure, while for the P-v diagram the critical point represents the critical temperature. On the T-v diagram when the pressure goes above the critical point then there will be no distinct phase change. Instead the substance will appear to remain as one phase as the specific volume increases until the substance resembles a vapor. Refer to the figure below.

Supercritical T-v diagram

P-v and T-v diagrams can also show the phase changes between all three phases. The figures below show the P-v diagrams for substance that has its solid phase contract during freezing and the P-v diagram for a substance that has its solid phase expand during freezing. An example of substance that has it solid phase expand during freezing is water.

P-v diagram contracting solid
P-v diagram expanding solid

From these diagrams it can be seen that at a low pressures it is possible for a solid to change directly into a vapor skipping the liquid phase. It is also possible for all three phases to exist together at the triple line. At the triple line the temperature and pressure will remain the same as the specific volume changes.

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