Notes on Temperature-Entropy Diagrams
Although chemical and mechanical engineer^',^ have long heen familiar with temperature-entropy diagrams, few instructors in physical chemistry make much use of them, except for a brief mention in discussing the Carnot cycle. Prof. Wood suggests that this is unfortunate, and that many useful concepts become more clear when displayed on s&h a diagram. He chooses for his example a one-component system in a two-phase region
existence curve. At temperatures below this, two phases exist along the horizontal portions of the isotherms, hut a t higher temperatures only one phase appears. The data from which the diagram of Figure 1 is plotted are susccpt,ible to direct experimental measuremont. Additional meaclurements make it DOSsible to calculate the entropy of a given mass of material as a function of temperature, pressure and/ or volume, using the equations
and
Figure 1. Preuure-volume diagram for a given quantity of a pure wbrtance, 3howing hotherms.
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Figure 2. Ikobors on a temperature-entropy diogram, rhowing the 0.2; q2 0.8. boundary of the two-phase system. qt
Since any two of the thermodynamic properties are sufficient to determine, for a substance of fixed composition, the properties of the system, a diagrtm displaying two of them on rectangular coordinates pcrmits one to erect surfaces displaying others. Often these surfaces are represented as cont'our lines, as, for example, the isot,herms of t,he usual pV diagrams. Chemists are familiar with the latter type of diagram for t,he liquid-vapor region (Fig. I). The isotherm T, a t the critical temperature just makes cont,act with the dashed line rcpresentiug the co-, HOWGI;N, 0.A,, .\Nn WATSON, K. X., "Chemical Process Principles," John Wiley h Sons, New York, 1947, Chap. 1> ' 12 --,
2 0 ~ ~ , :E.~ 1 F., , , "Internal Combustion Engines," (2nd Ed), International Textbook Co., Srranton, Pa., 1950, Chap. 3.
286 / Journal of Chemical Education
and a start,ing value, So, chosen for some specified temperature and pressure.' Such calculated results are plotted in Figure 1 of the paper, with isobars as contour lines on the surface erected on t,he planar diagram. Had Prof. Wood applied his diagram specifically to the liquid-vapor equilibrium of Figure 1, he could have added a dome-shaped curve separating the twophase region from the one-phase regions (Fig. 2). Thus, c represents t,he same point in both Figures 1 and 2, and the points a, b, d, and e could represent the same points. Once a plot such as Figure 2 has been prepared, various deductions from it can be made. In addition to those suggested by Prof. Wood relating entropy changes to changes in pressure and phase, Figure 2 shows that an adiabatic (isent:ropic)pressure decrease for a gas (expansion) must cool the gas (line m n ) . The dotted lines ql and qz in t,he two-phase region represent lines of equal "quality" of the vapor (equal ratios of mass of vapor to total mass). It is evident. that an isentropic temperature change in this region may either increase or decrease t,he quality, depending upon whether one starts near the left side of the dome-shaped curve; or near the right side. Frank H. Verhoek The Ohio State University Columbus, 43210
