# What do the horizontal lines in a P-V phase diagram mean?

I have been studying phase diagrams of pure substances, and for a substance such as carbon dioxide for example, it's diagram looks something like this:

The horizontal lines in the liquid phase puzzle me. It seems if we shrink the specific volume by a certain amount, the pressure change is much much less. This doesnt seem to be what is observed in reality (liquids have a very high bulk moduli and are generally considered incompressible), which would require a large pressure change for a less change in specific volume. The solid phase has vertical lines, which seems to be true, but the liquid portion baffles me.

The horizontal lines represent a combination of liquid and vapor at the same temperature and pressure. At the left of the horizontal line is the liquid specific volume and on the right side is the saturated vapor specific volume. Locations between the two ends represent the specific volume of the combination, which is proportional to the amount of each.

• You're right. The tie lines join the gas and liquid phases. I corrected my answer based on yours. Thank you for noting the error. – MaxW Jul 11 '19 at 21:54

the graph is trying to show three things (pressure, density and temperature) in 2D.

The yellow portion shows the super critical fluid of $$\ce{CO2}$$.

The blue portion liquid $$\ce{CO2}$$

The light green portion shows the gas phase for $$\ce{CO2}$$.

The horizontal lines are called "tie lines." The two phases at the ends of the tie lines are in equilibrium.

If you follow the line for say for 12 $$^\circ$$C, from the degree notation there is at first one phases, a gas phase.

Now when you reach the dotted curve there are two phases a gas phase and a liquid phase which are joined by a horizontal tie line.

The whole thing is a lot easier to figure out with a more traditional phase diagram.

Found above on page: https://www.engineeringtoolbox.com/CO2-carbon-dioxide-properties-d_2017.html

• Thanks for your answer, looks like I've been reading it wrong the whole time. Btw, which portion would be solid $\ce{CO2}$? – Pritt says Reinstate Monica Jul 12 '19 at 2:39
• Furthermore, does this mean that the tie-lines are just a diagrammatic representation, and not the actual relation between pressure and specific volume (reducing volume doesnt increase pressure by alot) – Pritt says Reinstate Monica Jul 12 '19 at 2:42
• No solid Co2 on your diagram. Look at the lower one. You have to get to about -55 C to get solid CO2. // Quote "The horizontal lines are called "tie lines." The two phases at the ends of the tie lines are in equilibrium." – MaxW Jul 12 '19 at 6:16
• @PrittBalagopal If I understand correctly, along a tie line, you can increase and decrease specific volume without changing the pressure, because these parts of the diagram represent mixtures of liquid and gas. Increasing the specific volume will cause some of the liquid to evaporate, and decreasing the specific volume will cause some of the gas to condense; in either case, the equilibrium pressure remains the same. – Tanner Swett Jul 12 '19 at 12:16
• @PrittBalagopal I think so. The left end of the tie line is where all of the gas has condensed, so you're left with only liquid, and the right end is where all of the liquid has evaporated, and you're left with only gas. That's my understanding; hopefully someone else can confirm. – Tanner Swett Jul 12 '19 at 13:48

The horizontal lines are tie-lines, as explained in another answer, but between gas and liquid $$\ce{CO_2}$$. Note the curves labeled with temperatures lie below the critical temperature and above the triple point. The horizontal lines therefore represent regions where gas and liquid $$\ce{CO_2}$$ coexist. The single point at the cusp of the dotted line is the critical point. At points on a tie-line you can use the lever rule to determine the fraction of liquid and gas from the corresponding distances to the dotted lines on the two ends of the tie-line. The volume at points on the tie line is an average over the two phases. The fact that the pressure (and temperature) are constant on a tie-line is consistent with out understanding of a first order phase transition.

I recommend searching online for another clearer version of the phase diagram.

• You're right. The tie lines join the gas and liquid phases. I corrected my answer based on yours. Thank you for noting the error. – MaxW Jul 11 '19 at 21:55