Document wgekoeanGVOqEGwe97or1QB04

HEATING VENTILATING AIR CONDITIONING CUIDE 1944 The earliest investigation into the relation between pressure, specific volume, and temperature for gases was made by Boyle (1661) who was able to confirm the hypothesis that the volume of a given weight of gas should, vary inversely as the absolute pressure if temperature is main tained constant. Thus, within the limits of his experimental error Boyle found that at constant temperature the product pv, pressure times specific volume, has a constant value over a considerable range of pressures. These results are best visualized by plotting values of the product pv as ordinate against values of pressure p itself as abscissa. According to Boyle's experimental findings lines of constant temperature (isotherms) of a gas are straight and horizontal on this pv, p-plane. The first rough experiments of Charles (1787) and the subsequent more refined experiments of Gay-Lussac (1802) suggested the possibility Table 1. Composition of Dry Air Gas Mol per Mol Dry Air Lb per Mol Lb per Mol Dry Air Lb Per Lb 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 C X 2.016 X 39.944 21.861 6.717 0.013 0.000 0.376 28.967 0.7547 0.2319 0.0004 0.0000 0.0130 , 1.0000 Argon__ Neon___ Helium... Krypton. Xenon__ Composition of Argon 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, p> = 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 2 CHAPTER 1. THERMODYNAMICS OF AIR AND WATER MIXTURE 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. MT) = a temperature function called second virial 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 aggregate is equal to the mean value of a quantity, which Clausius called the virial 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 gases, 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 specific volume 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 oT 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 -v- 28.967 = 53.351 Bw = 1545.4 -r* 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 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 Bracketed numbers refer to references at end of chapter. 3