# Shape of isotherms in $P$-$V$ phase diagram

Please explain the shape of the isotherms in this P-V phase diagram. In particular, why are the isotherms flat in the liquid-vapor region?

(image from Lumen Learning | Physics | Phase Changes)

In this region of the $$P$$-$$V$$ diagram liquid and gas phase coexist. That means

• some of the liquid can evaporate and become gas,
• or some of the gas can condense and become liquid

while the pressure $$P$$ and temperature $$T$$ don't change.

Because of the different densities of liquid and gas this happens with a big change of volume $$V$$.

That's why in the $$P$$-$$V$$ diagram the isothermal lines (i.e. $$T = \text{const}$$) are flat lines. When moving along such a line the percentages of liquid and gas change, while the total amount of substance of course stays the same. On the left edge of the blue area there is 100% liquid, and on the right edge there is 100% gas.

The isotherms are flat because during the phase transition takes place in such a way that the pressure remains constant. This means that the Gibbs free energy of either phases are the same.

During the phase transition the pressure and temperature are dependent on each other, and the constant pressure at which the transition takes place is called the saturation pressure. For a particular value of temperature, only one value of pressure allows the transition to take place. So the entire transition region (i.e. the liquid-vapor region) is actually a curve in the V-T plane.

Because in that region the pressure can be held constant while the relative volumes of vapor and liquid can vary for the same total amount of fluid in the system.

• Thanks. Another quick question: How do we know in which direction the temperature of the isotherms is increasing? – Thomas Jul 12 '19 at 8:35
• What is the meaning of "isotherm"? As lines of constant temperature, it neither increases or decreases... – user207455 Jul 12 '19 at 8:36
• No, I meant the temperatures of different isotherms... – Thomas Jul 12 '19 at 9:00
• The isotherms increase in temperature as the pressure and/or volume increase. Which is why you get the flat bit when the pressure is constant. – user207455 Jul 12 '19 at 9:01