Thermodynamics

22 | ThermodynamicsP = 3 psi150 poundsA feet = 50 in 2P = 6 psi 300 poundsP = s ––––W––––––150 lbfn = =A feet 50 in 2 = 3 psiFIGURE 1–36The normal stress (or “pressure”) onthe feet of a chubby person is muchgreater than on the feet of a slimperson.FIGURE 1–37Some basic pressure gages.Dresser Instruments, Dresser, Inc.Used by permission.The pressure unit pascal is too small for pressures encountered in practice.Therefore, its multiples kilopascal (1 kPa 10 3 Pa) and megapascal (1MPa 10 6 Pa) are commonly used. Three other pressure units commonlyused in practice, especially in Europe, are bar, standard atmosphere, andkilogram-force per square centimeter:1 bar 10 5 Pa 0.1 MPa 100 kPa1 atm 101,325 Pa 101.325 kPa 1.01325 bars1 kgf>cm 2 9.807 N>cm 2 9.807 10 4 N>m 2 9.807 10 4 Pa 0.9807 bar 0.9679 atmNote that the pressure units bar, atm, and kgf/cm 2 are almost equivalent toeach other. In the English system, the pressure unit is pound-force per squareinch (lbf/in 2 , or psi), and 1 atm 14.696 psi. The pressure units kgf/cm 2and lbf/in 2 are also denoted by kg/cm 2 and lb/in 2 , respectively, and they arecommonly used in tire gages. It can be shown that 1 kgf/cm 2 14.223 psi.Pressure is also used for solids as synonymous to normal stress, which isforce acting perpendicular to the surface per unit area. For example, a 150-pound person with a total foot imprint area of 50 in 2 exerts a pressure of 150lbf/50 in 2 3.0 psi on the floor (Fig. 1–36). If the person stands on one foot,the pressure doubles. If the person gains excessive weight, he or she is likelyto encounter foot discomfort because of the increased pressure on the foot(the size of the foot does not change with weight gain). This also explainshow a person can walk on fresh snow without sinking by wearing largesnowshoes, and how a person cuts with little effort when using a sharp knife.The actual pressure at a given position is called the absolute pressure, andit is measured relative to absolute vacuum (i.e., absolute zero pressure). Mostpressure-measuring devices, however, are calibrated to read zero in the atmosphere(Fig. 1–37), and so they indicate the difference between the absolutepressure and the local atmospheric pressure. This difference is called the gagepressure. Pressures below atmospheric pressure are called vacuum pressuresand are measured by vacuum gages that indicate the difference between theatmospheric pressure and the absolute pressure. Absolute, gage, and vacuumpressures are all positive quantities and are related to each other byP gage P abs P atm(1–15)P vac P atm P abs(1–16)This is illustrated in Fig. 1–38.Like other pressure gages, the gage used to measure the air pressure in anautomobile tire reads the gage pressure. Therefore, the common reading of32 psi (2.25 kgf/cm 2 ) indicates a pressure of 32 psi above the atmosphericpressure. At a location where the atmospheric pressure is 14.3 psi, for example,the absolute pressure in the tire is 32 14.3 46.3 psi.In thermodynamic relations and tables, absolute pressure is almost alwaysused. Throughout this text, the pressure P will denote absolute pressureunless specified otherwise. Often the letters “a” (for absolute pressure) and“g” (for gage pressure) are added to pressure units (such as psia and psig) toclarify what is meant.