Chapter S-INTRODUCTION TO THERMODYNAMICS 



The significance of some of the lines on this 

 diagram will become clearer as we consider 

 some of the related two-dimensional diagrams. 



Three-dimensional diagrams are extremely 

 useful in giving an overall picture of the p-v-T 

 relationships, but they are difficult to construct 

 and are somewhat difficult to use for detailed 

 analysis. Two-dimensional graphs are fre- 

 quently projected from the three-dimensional 

 p-v-T surfaces. Even on a two-dimensional dia- 

 gram, a great many relationships of properties 

 can be indicated by means of contour lines or 

 superimposed curves. 



The p-v diagram is made by plotting known 

 values of pressure (p) along the ordinate and 

 values of specific volume (v) along the ab- 

 scissa.^® To illustrate the construction of a 

 p-v diagram, let us consider the isothermal 

 compression of 1 pound of air from an initial 

 pressure of 1000 pounds per square foot absolute 

 to a final pressure of 6000 psfa. Let us assume 

 that the air is at a temperature of 90° F, or 550° 

 R. Since we may treat air asaperfect gas under 

 these conditions of pressure and temperature, we 

 may use the laws of perfect gases and the equa- 

 tion 



where 



pv = RT 



p = absolute pressure, psfa 

 V = specific volume, cu ft per lb 

 R = gas constant (53.3 for air) 

 T = absolute temperature, °R 



Since the compression is isothermal, T is 

 constant and the expression RT is equal to 

 53.3 X 550, or 29,315. It is apparent from the 

 equation that p and v must vary inversely— that 

 is, as p goes up, v goes down. Hence, for any 

 given value of p we may find a value of v merely 

 by dividing 29,315 by p. Choosing six values of 

 p and computing the values of y, we obtain the 

 following values: 



STATE A 

 STATE B 

 STATE C 

 STATE D 

 STATE E 

 STATE F 



p = 1000, V = 29.3 

 p = 2000, V = 14.7 

 p = 3000, V = 9.8 

 p = 4000, V = 7.3 

 p = 5000, V = 5.9 

 p = 6000, V = 4.9 



By plotting these values on graph paper, we 

 obtain the p-v diagram shown in figure 8-14. 

 The curve applies only to the indicated tempera- 

 ture— that is, it is an isothermal curve. The 

 values of p and _v may be calculated for the same 

 process at other temperatures, and plotted as 

 before; in this case we obtain a series of iso- 

 thermal curves (or isotherms) such as those 

 shown in figure 8-15. 



A p-v diagram for water and steam is shown 

 in figure 8-16. This diagram— and, in fact, most 

 diagrams for real substances in the region of a 

 state change— is not drawn to scale because of the 

 very great difference in the specific volume of 

 the liquid and the specific volume of the vapor. 

 Even though it is not drawn to scale, the p-v 

 diagram serves a useful purpose in indicating 

 the general configuration of the saturated liquid 

 line and the saturated vapor line. These lines, 

 which are called process lines , blend smoothly 

 at the critical point. The shape formed by the 

 process lines is characteristic of water and will 

 be observed on all p-v diagrams of this sub- 

 stance. 



A two-dimensional pressure-temperature 

 (p-T) diagram of the type shown in figure 8-17 

 is useful because it indicates the way in which 

 the phase of a substance depends upon pressure 

 and temperature. The solid-liquid curve, for 

 example, indicates the effects of pressure on 



10 15 20 25 30 35 40 45 

 VOLUME (CUBIC FT PER LB) 



The p-v diagram, as it applies to internal combus- 

 tion engines, is discussed further in chapter 22 of this 

 text. 



147.67 

 Figure 8-14.— Constant temperature (isothermal) 

 line on p-v diagram. 



187 



