so on the left the curve is very steep as shown. The shaded area under the gold dashed line represents the region where the gas and liquid phases exist together in equilibrium. Curve C in Fig. 13 – 21 represents the behavior of the substance at its critical temperature ; the point c (the one point where curve C is horizontal) is called the critical point . At temperatures less than the critical temperature, a gas will change to the liquid phase if sufficient pressure is applied. Above the critical tempera- ture (and this is the definition of the term), no amount of pressure can cause a gas to change phase and become a liquid. (Thus curves A and B represent the sub- stance at temperatures where it can only be a gas.) The critical temperatures for various gases are given in Table 13 – 2. Scientists tried for many years to liquefy oxygen without success, which led to the idea that there must be a critical point. Oxygen can be liquefied only if first cooled below its critical temperature of – 118°C. B ¿ PV = constant. A ¿ T D . T C , T B , T A , PV = NkT TABLE 13–2 Critical Temperatures and Pressures Critical Temperature Critical Pressure Substance °C K (atm) Water 374 647 218 31 304 72.8 Oxygen 118 155 50 Nitrogen 147 126 33.5 Hydrogen 239.9 33.3 12.8 Helium 267.9 5.3 2.3 – – – – CO 2
Often a distinction is made between the terms “gas” and “vapor”: a substance below its critical temperature in the gaseous state is called a vapor ; above the critical temperature, it is called a gas . The behavior of a substance can be diagrammed not only on a PV diagram but also on a PT diagram. A PT diagram , often called a phase diagram , is particu- larly convenient for comparing the different phases of a substance. Figure 13 – 22 is the phase diagram for water. The curve labeled represents those points where the liquid and vapor phases are in equilibrium — it is thus a graph of the boiling point versus pressure. Note that the curve correctly shows that at a pres- sure of 1 atm the boiling point is 100°C and that the boiling point is lowered for a decreased pressure. The curve represents points where solid and liquid exist in equilibrium and thus is a graph of the freezing point versus pressure. s - l l - v 378 CHAPTER 13 Temperature and Kinetic Theory P (atm) T ( ° C) 31 5.11 Solid Liquid Triple point Critical point 20 − 56.6 1 56 73 Vapor s - v s - l l - v FIGURE 13–23 Phase diagram for carbon dioxide. T ( ° C) P (atm) 100 1.0 218 0.006 374 0.01 0.00 Solid Liquid Vapor Triple point Critical point s - v l - v s - l Gas FIGURE 13–22 Phase diagram for water (note that the scales are not linear). At 1 atm, the freezing point of water is 0°C, as shown. Notice also in Fig. 13 – 22 that at a pressure of 1 atm, the substance is in the liquid phase if the temperature is between 0°C and 100°C, but is in the solid or vapor phase if the temperature is below 0°C or above 100°C. The curve labeled s- v is the sublimation point versus pressure curve. Sublimation refers to the process whereby at low pressures a solid changes directly into the vapor phase without passing through the liquid phase. For water, sublimation occurs if the pressure of the water vapor is less than
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