Document G5MwQDBjJL5dKYGw9ppB2Gjbm

2 Chapter 1 Table 1. Composition of Dry Air Gas Mol per Mol Dry Air Lb. pbr Mol Lb per Mol Dry Air Nitrogen____________ Oxygen___ ___ _ Carbon Dioxide.. Hydrogen.................... Argon........................... 0.7803 0.2099 0.0003 0.0001 0.0094 1.0000 X 28.016 X 32.000 X 44.003 X 2.016 X 39.944 21.861 6.717 0.013 0.000 0.376 - 28.967 1945 Guide Lb per Lb * Dry Air 0.7547 0.2319 0.0004 0.0000 0.0130 1.0000 Composition op Argon Argon_______ ___ Neon___________ Helium_________ Krypton________ Xenon.-. Mol per Mol Dry Air 0.00933 0.000018 0.000005 0.000001 0.00935 of establishing a universal temperature scale such that the product pv for any gas is simply proportional to temperature measured on this scale in accordance with Equation 1, pv = BT (1) where B is a constant characteristic of the given gas. Referring to the graphical representation previously described in which the product pv is plotted as ordinate against pressure p as abscissa, the vertical spacing of the isotherms should be such that the ordinates to any two isotherms are in the ratio of corresponding absolute temperatures and therefore in the same ratio for any gas. Precise measurements by modern methods have shown that the experi mental findings of Boyle, Charles and Gay-Lussac are only approximately correct. In the range of sufficiently low pressures the isotherms of gases are indeed straight on the pv, -plane; but they are not horizontal in accordance with Boyle's Law, being inclined downward to the right at relatively low temperatures, upward to the right at higher temperatures. Extrapolation of each isotherm to zero pressure has revealed the remark able fact that the limiting value of the product pv thus obtained is strictly , proportional to absolute temperature as suggested by Equation 1, this strict proportionality providing an accurate basis for the establishment of the absolute temperature scale. ' The experimental facts of the preceding paragraph are expressed mathematically by Equation 2, pv'= BT -- A(T) p (2) where p = absolute pressure, pounds per square foot. v = specific volume, cubic feet per pound. B = a constant depending on the molecular weight of the gas. T = absolute temperature, degrees Fahrenheit. A(T) = a temperature function called second viridl coefficient, cubic feet per pound [2].* The name undoubtedly, originated from consideration of Clausius' Virial Theorem according to which the mean kinetic energy of a molecular Bracketed numbers refer to references at end of chapter. Thermodynamics of Air and Water Mixtures _______ ;3 aggregate is equal to the mean value of a quantity, which Clausius called - the mrial of the system, depending solely on the forces acting upon the molecules and' not upon the motion of the molecules. This name is used ' extensively. For some eases, the magnitude of the second, virial coefficient can be predicted from theory; but, at present, direct experimental measure ments are more reliable. . It will appear in what follows that the error committed in computing values of specificvolume from Equation 1 instead of Equation 2 is extremely small. Thermodynamically, however, the former would deny the effect of pressure on the thermal properties of a gas which experiment shows to be appreciable. Therefore Equation 1 cannot be made the basis of an accurate analysis. The numerical value of the constant B in Equation 2 is different for every different gas, but can be calculated if the molecular weight m, pounds per mol, is known; for the product mB is a universal gas con stant R, namely, R = 1545.4 Example 1. Find the value of B for dry air and water vapor. Solution. . Ba = 1545.4 -5- 28.967 = 53.351 Bw = 1545.4 H- 18.0154 = 85.782 The temperature function A (T), the so-called second virial coefficient, expresses the effect of intermolecular forces. It is positive at low tem- Temp F t -96 -64 -32 0 Table 2. Specific Volume of Dry Air at 29.921 In. Hg Cu Ft per fl Lb H Pa | 9.1488 9.9597 10.7699 f 11.5796 Temp F t 32 64 96 128 Cu Ft per Lb Pa 12.3888 13.1977 14.0063 14.8147 Temp F t 1 160 192 224 256 Cu Ft per Lb * 15.6229 16.4310 17.2389 19.0467 . aPrepared by John A. Goff. peratures where these forces are predominantly attractive, negative at higher temperatures where they are predominantly repulsive. It is known with satisfactory accuracy for both dry air and water vapor. Values of specific volume are listed in Table 2 for dry air at standard atmospheric pressure (29.921 in. Hg) as' computed from Equation 2. The fact that A{T) is multiplied by pressure in Equation 2 means . that intermolecular forces vanish at zero pressure and infinite volume where infinite distances separate the molecules. The finite value of the product pv at zero pressure is due entirely to the translational kinetic energy of the molecules. In ordinary calculations not requiring too great accuracy, the effect of intermolecular forces may be ignored and Equation 2 simplified to pv = BT (1) Example 2. Calculate an approximate value for the specific volume of dry air at 64 F, 29.921 in. Hg. Scoiiuhon. v = ^9 95213.3x510 X495U253.7X0H4 = 13.n2o0n0 cu nft per pound. . Note:: This answer may be .compared with the value in Table 2. The difference is due to intermolecular forces. It should not be concluded, however, that because the effect of intermolecular forces on the volume is so small these forces can be ignored entirely. !'