Single-Component P-V and T-V Diagrams

The van der Waals equation of state for water is used to generate isotherms on a pressure-log volume (
P-V
) diagram and isobars on a temperature-log volume (
T-V
) diagram. Use sliders to change the isotherm temperature on the
P-V
diagram and the isobar pressure on the
T-V
diagram. Liquid and vapor are in equilibrium within the phase envelope, which is generated from data for water. The isotherms and isobars have three solutions in the two-phase region, but the only physically-meaningful conditions are the orange dots, which correspond to saturated liquid and saturated vapor. The saturated liquid volume
L
V
and the saturated vapor volume
V
V
are displayed. The horizontal, dashed orange line (at
sat
P
and
sat
T
) represents a mixture of liquid and gas. On the
P-V
diagram, the green area above the orange line is equal to the area below the orange line when plotted on a linear volume scale.

Details

Isotherms and isobars are solved using the Van der Waals equation of state:
P=
RT
V-b
-
a
2
V
,
rearranged:
T=
1
R
P+
a
2
V
(V-b)
,
a=
27
64
2
R
2
T
c
P
c
,
b=
R
T
c
8
P
c
,
where
P
is pressure (MPa),
R
is the ideal gas constant (
[MPa
3
cm
]/[molK]
),
T
is temperature (K),
V
is molar volume (
3
cm
/mol
),
a
and
b
are van der Waals constants,
T
c
is the critical temperature of water (K), and
P
c
is the critical pressure (MPa).
The screencast video at[1] explains how to use this Demonstration.

References

[1] Single-Component P-V and T-V Diagrams. www.colorado.edu/learncheme/thermodynamics/SingleComponentPVTVdiagrams.html.

External Links

Van der Waals Isotherms

Permanent Citation

Rachael L. Baumann, John L. Falconer
​
​"Single-Component P-V and T-V Diagrams"​
​http://demonstrations.wolfram.com/SingleComponentPVAndTVDiagrams/​
​Wolfram Demonstrations Project​
​Published: September 16, 2014