Thermodynamics

cen84959_ch03.qxd 4/26/05 4:40 PM Page 138138 | ThermodynamicsPer unit massv, m 3 /kgu, kJ/kgh, kJ/kgPer unit molev, m 3 /kmolu, kJ/kmolh, kJ/kmolFIGURE 3–46Properties per unit mole are denotedwith a bar on the top.FIGURE 3–47The ideal-gas relation often is notapplicable to real gases; thus, careshould be exercised when using it.© Reprinted with special permission of KingFeatures Syndicate.called molecular weight) of the gas. The constant R u is the same for all substances,and its value isR u 7898.31447 kJ>kmol # K8.31447 kPa # m 3 >kmol # K0.0831447 bar # m 3 >kmol # K1.98588 Btu>lbmol # R10.7316 psia # ft 3 >lbmol # R1545.37 ft # lbf>lbmol # R(3–11)The molar mass M can simply be defined as the mass of one mole (alsocalled a gram-mole, abbreviated gmol) of a substance in grams, or the massof one kmol (also called a kilogram-mole, abbreviated kgmol) in kilograms.In English units, it is the mass of 1 lbmol in lbm. Notice that the molarmass of a substance has the same numerical value in both unit systemsbecause of the way it is defined. When we say the molar mass of nitrogen is28, it simply means the mass of 1 kmol of nitrogen is 28 kg, or the mass of1 lbmol of nitrogen is 28 lbm. That is, M 28 kg/kmol 28 lbm/lbmol.The mass of a system is equal to the product of its molar mass M and themole number N:m MN1kg2(3–12)The values of R and M for several substances are given in Table A–1.The ideal-gas equation of state can be written in several different forms:V mv ¡ PV mRTmR 1MN2R NR u ¡ PV NR u TV Nv ¡ Pv R u T(3–13)(3–14)(3–15)where v is the molar specific volume, that is, the volume per unit mole (inm 3 /kmol or ft 3 /lbmol). A bar above a property denotes values on a unit-molebasis throughout this text (Fig. 3–46).By writing Eq. 3–13 twice for a fixed mass and simplifying, the propertiesof an ideal gas at two different states are related to each other byP 1 V 1T 1 P 2V 2T 2(3–16)An ideal gas is an imaginary substance that obeys the relation Pv RT(Fig. 3–47). It has been experimentally observed that the ideal-gas relationgiven closely approximates the P-v-T behavior of real gases at low densities.At low pressures and high temperatures, the density of a gas decreases,and the gas behaves as an ideal gas under these conditions. What constituteslow pressure and high temperature is explained later.In the range of practical interest, many familiar gases such as air, nitrogen,oxygen, hydrogen, helium, argon, neon, krypton, and even heaviergases such as carbon dioxide can be treated as ideal gases with negligibleerror (often less than 1 percent). Dense gases such as water vapor in steampower plants and refrigerant vapor in refrigerators, however, should not betreated as ideal gases. Instead, the property tables should be used for thesesubstances.