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# 19.4: pV-Diagrams

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CONTENTS

### 19.4: pV-Diagrams

The pV diagram, which is a graph of pressure versus volume of the gas under study, is helpful in describing certain aspects of the substance. When the substance behaves like an ideal gas, the ideal gas equation describes the relationship between its pressure and volume. On a pV diagram, it is common to plot an isotherm, which is a curve showing p as a function of V with the number of molecules and the temperature fixed. Then, for an ideal gas, the product of the pressure of the gas and its volume is constant. For example, the volume of the gas decreases as the pressure increases. The resulting pV graph is a hyperbola.

pV isotherms are hyperbolic at high temperatures and low pressures. As we cool the gas, the pV graph deviates from hyperbola.  At a critical temperature (Tc), pV curve shows a point with zero slope. As the gas is cooled further, pV curve starts to display a region of zero slope. Within this region, the volume of gas changes, but that does not change its pressure. This behavior corresponds to boiling and condensation; when a substance is at its boiling temperature for a particular pressure, it can increase in volume as some of the liquid turns to gas (moving from lower volume to higher volume) or decrease as some of the gas turns to liquid (moving from higher volume to lower volume), without any change in temperature or pressure. This is the region where vaporization or liquification takes place.

The steep parts of the curves to the left of the transition region show the liquid phase, which is almost incompressible—a slight decrease in volume requires a significant increase in pressure. The flat parts show the liquid-gas transition, representing combinations of pressure and volume where liquid and gas can coexist. The right of the transition region shows the gas phase.

The isotherms above Tc do not go through the liquid-gas transition. Therefore, liquid cannot exist above that temperature, the critical temperature. At sufficiently low pressure above that temperature, the gas has the density of a liquid but will not condense; the gas is said to be supercritical.  At higher pressure, it is solid. Carbon dioxide, for example, has no liquid phase at a temperature above 31 degrees Celsius. The critical pressure is the maximum pressure at which the liquid can exist. The point on the pV diagram at the critical pressure and temperature is the critical point.