# On the dielectric constants of liquid and vapor phases of a material

I can find the static dielectric constant of materials on the website or in a handbook. But for some liquids, it only shows the dielectric constant at the saturation vapor pressure. I am confused that if the dielectric constant is the same for the liquid and gas phase, see the following figure for example. (I guess it should be very different.) If the electric conductivities are different for the gas phase and liquid phase of the same material, should the dielectric constants be also different?

As can be seen in the following table about the properties of water and steam as a function of temperature (taken from CRC handbook). A duplicate entry in the temperature column indicates a liquid-vapor phase transition at that temperature; property values are then given for both phases.

Is there a table that gives the dielectric constants for both the gas and liquid phases of a material, for example, C$$_2$$HCl$$_2$$F$$_3$$. Thank you in advance!

The dielectric constants are extremely different for the liquid and gas phases. Just look at the table for water.

Contrary to the table for C$$_2$$HCl$$_2$$F$$_3$$ which indeed has chosen to mention only the liquid phase at the saturation vapor pressure, the table for water gives a list the dielectric constant at many temperatures for two values of the pressure, first 0.1 MPa and then 1 MPA.

When the temperature crosses the value for which each of these pressures corresponds to the saturation vapor pressure at that temperature (372.76 K and 453.03 K respectively), the only temperature where gas and liquid coexist at that pressure, it gives two values, one large value corresponding to the liquid, and one very close to unity, less then 1.1 in all cases, corresponding to gas.

Above the temperature where the saturation vapor pressure is just 0.1 MPa or 1 Mpa respectively, only the gas phase can exist and thus the dielectric constant is always less than 1.1 and decreases towards 1.

I suppose that if the table for C$$_2$$HCl$$_2$$F$$_3$$ which only gives the dielectric constant precisely at the temperature where both phases do exist gives only a large value, obviously that of the liquid, it is because whoever published this table considered that the dielectric constant for the gas is so close to 1 that its precise value is of no practical interest, and one can assume it is equal to 1 for all practical purposes.

One can remark that when the pressure increases from 0.1 MPa to 1 MPa and thus the temperature at the saturation vapor pressure is precisely that pressure also increases, the difference, while still very large, is somewhat less large : the dielectric constant of the liquid drops from about 55 to less than 40, that of the gas increases from 1.006 to 1.042, still close to 1 but seven times farther from 1 than at the lower pressure. When the pressure keeps increasing, and the temperature at which this pressure coincide with the saturation vapor pressure also keeps increasing, this trend keeps going on. When one gets close to the critical point beyond which there is only one phase, the values for the liquid and gas phases get closer and closer and finally coincide at the critical point. For water that would happen at 22.1 MPa and 647.1 K and the value of the dielectric constant is about 6 (common, since all the differences between the two phases disappear at the critical point).

I have no idea what the critical point of C$$_2$$HCl$$_2$$F$$_3$$ is, but I suppose the critical pressure is sufficiently above 0.2 MPa and the critical temperature sufficiently above 323 K that the dielectric constant of the gas phase is still very close to 1 for all the cases mentioned in the table. Otherwise they would have given it !