<em>PV</em> Diagrams
PV Diagrams
We can examine aspects of the behavior of a substance by plotting a graph of pressure versus volume, called a PV diagram. When the substance behaves like an ideal gas, the ideal gas law describes the relationship between its pressure and volume. That is,
Now, assuming the number of molecules and the temperature are fixed,
For example, the volume of the gas will decrease as the pressure increases. If you plot the relationship \(\text{PV}=\text{constant}\) on a \(\text{PV}\) diagram, you find a hyperbola. The figure below shows a graph of pressure versus volume. The hyperbolas represent ideal-gas behavior at various fixed temperatures, and are called isotherms. At lower temperatures, the curves begin to look less like hyperbolas—the gas is not behaving ideally and may even contain liquid. There is a critical point—that is, a critical temperature—above which liquid cannot exist. At sufficiently high pressure above the critical point, the gas will have the density of a liquid but will not condense. Carbon dioxide, for example, cannot be liquefied at a temperature above \(\text{31}\text{.}0\text{º}\text{C}\). Critical pressure is the minimum pressure needed for liquid to exist at the critical temperature. The table below lists representative critical temperatures and pressures.
\(\text{PV}\) diagrams. (a) Each curve (isotherm) represents the relationship between \(P\) and \(V\) at a fixed temperature; the upper curves are at higher temperatures. The lower curves are not hyperbolas, because the gas is no longer an ideal gas. (b) An expanded portion of the \(\text{PV}\) diagram for low temperatures, where the phase can change from a gas to a liquid. The term “vapor” refers to the gas phase when it exists at a temperature below the boiling temperature.
Critical Temperatures and Pressures
| Substance | Critical temperature | Critical pressure | ||
|---|---|---|---|---|
| \(\text{K}\) | \(\text{º}\text{C}\) | \(\text{Pa}\) | \(\text{atm}\) | |
| Water | 647.4 | 374.3 | \(\text{22}\text{.}\text{12}×{\text{10}}^{6}\) | 219.0 |
| Sulfur dioxide | 430.7 | 157.6 | \(7\text{.}\text{88}×{\text{10}}^{6}\) | 78.0 |
| Ammonia | 405.5 | 132.4 | \(\text{11}\text{.}\text{28}×{\text{10}}^{6}\) | 111.7 |
| Carbon dioxide | 304.2 | 31.1 | \(7\text{.}\text{39}×{\text{10}}^{6}\) | 73.2 |
| Oxygen | 154.8 | −118.4 | \(5\text{.}\text{08}×{\text{10}}^{6}\) | 50.3 |
| Nitrogen | 126.2 | −146.9 | \(3\text{.}\text{39}×{\text{10}}^{6}\) | 33.6 |
| Hydrogen | 33.3 | −239.9 | \(1\text{.}\text{30}×{\text{10}}^{6}\) | 12.9 |
| Helium | 5.3 | −267.9 | \(0\text{.}\text{229}×{\text{10}}^{6}\) | 2.27 |
This lesson is part of:
Temperature, Kinetic Theory, and Gas Laws