Part II. Pressure Measurements in the Range from 10 2 Pa to 10 8 Pa

Transcription

1 Part II Pressure Measurements in the Range from 10 2 Pa to 10 8 Pa

2 Introduction The pressure range Pa has been selected as it is the interval covering the highest variety of interests and applications in gas temperature and pressure measurements. Particularly, at low temperatures several gas-based types of thermometry require the most accurate pressure measurements possible to realize their potentials in terms of high accuracy. Triple-point pressure determinations require measurements, typically from a few pascals (e.g., n-butane, K and 0.4 Pa) to a few mega pascal (e.g., carbon dioxide, K and MPa), of the highest possible accuracy, frequently involving the direct use of pressure primary standards. Vapor-pressure measurements of pure substances are performed mostly in the same pressure range (Fig. 4.1) and the helium-3 melting curve lies in the 3--4 MPa range. Gas thermometry extends typically from 1 to 200 kpa and is the most demanding as to accuracy. The determination of the critical point of gases and substances of interest, such as water, requires pressure measurements extending from 0.2 MPa to about 22 MPa. The critical point of helium-4 is at 5.2 K and 0.22 MPa, and that of water is at K and MPa. Considerations of scientific interest are gas compressibility determination, the study of pressure effects on temperature measurements by secondary standards, the equation of state of gases, transport properties, and many others. Industrial applications, which are very numerous in the range examined here, led us to extend the limit of the present survey to 100 MPa. The international unit of pressure of the Systeme International S.1. is the pascal (Pa), defined as a force of 1 N applied to a surface of 1 m 2 ; therefore 1 Pa = 1 N m -2. In this book we shall use only the pascal and its multiples, like the kilo pascal (kpa) and mega pascal (MPa). Another recognized pressure unit is the bar (1 bar = 10 5 Pa). All other units (mm Hg, mm H 20, at, atm, kg f em -2, psi) should be avoided and will not be used. The mm Hg unit, however, is still internationally accepted only in blood pressure measurements, owing to its very large diffusion and to the problems involved in the use of the S.1. unit (e.g., hectopascal or kilo pascal ). In meteorology the hectopascal (1 hpa = 1 mbar) is widely used. 265

3 List of Symbols Chapter 7 P Po Patm Pv Pj pz LJp PL t T t ref p/(t,p) Po p(t, Pat) p(t, (p + Po}/2) or PHg(t, (p + Po)/2) Pgas(t, p) Pa y(t) 1J(t,p) h Pressure Vacuum reference pressure Atmospheric pressure Mercury vapor pressure Operating value of the jacket pressure in a controlled clearance piston-cylinder unit Jacket pressure value for zero clearance Differential pressure Line pressure Temperature expressed in C Temperature expressed in K Reference temperature (generally 20 C) Density of a fluid Mercury density at 20 C and Pa Mercury density at temperature t and pressure Pat = Pa Mercury density at temperature t and at average pressure between P and Po Density of a gas at temperature t and pressure p (e.g., for nitrogen it will be PN2( t, p) Air density Surface tension of a fluid at temperature t Dynamic viscosity of a fluid at temperature t and pressure p Local acceleration of gravity Difference in height between liquids (case of liquid columns), or distance of a reference level from a fixed position (case of piston gauges) Relative humidity (h = 0.5 represents a rate of relative humidity of 50 % ) 267

4 268 H U S V and Vo KT Ks n(t, p) N A Av Cj c L lor 10 K Hg M R micon pm icon F AO(tref, Palm) Ae(t, p) h(x) '0 U(X) List of Symbols Helmoltz thermodynamic free energy Internal energy Entropy Volumes Isothermal compressibility Adiabatic compressibility Refractive index (gaseous media must be specified) Number of interferometric fringes Wavelength of a light source in a gas media Wavelength of a light source in vacuum Refractive index correction Speed of sound in mercury Length Engagement length of a piston in a cylinder Mercury compressibility Molar mass of a gas Gas constant (R= J mol- 1 K- 1 ) (Cohen and Taylor, 1986) Mole fraction of water vapor Mole fraction of carbon dioxide Compressibility factor for moist air (see Table F.4) Mass of the ith weight piece referred to its density pmj Density of the ith weight Conventional mass value referred to the conventional density pm icon Conventional density (8000 kg m -3) Gravitational force Effective area of a piston--cylinder unit measured at the reference temperature tref and at atmospheric pressure Palm Pressure distortion coefficient of a piston--cylinder unit (case of piston gauges) Pressure distortion coefficient of the piston (case of controlled clearance piston gauges) Linear thermal expansion coefficients of a piston and cylinder, respectively Effective area of a piston--cylinder unit at temperature t and pressure P Radial clearance for a piston--cylinder unit at the position x=o. Radial clearance for a piston--cylinder unit at the position x (x can change between 0 and L) Piston radius at the position x = 0 Piston deviations from the ideal reference radius

5 List of Symbols rc rp Rc Ap(t, Patm) d Psv(t) f(p, t) G Cylinder deviations from the ideal reference radius Radial displacements (generally on the outer surface of a cylinder) Poisson coefficients for piston and cylinder, respectively Elasticity moduli (Young) for piston and cylinder, respectively A verage inner radius of the cylinder Average radius of the piston Average outer radius of the cylinder Effective area of the piston at temperature t and atmospheric pressure Jacket pressure coefficient in a controlled clearance piston-cylinder unit Effective area of a controlled clearance piston-cylinder unit at pressure p, temperature t, and jacket pressure Pj Added mass on a piston gauge during differential pressure calibration, typically at a high line pressure Estimated variance Estimated standard deviation (it can be related to a fitting or to a number of repeated measurements of a physical quantity, or to the combination of different a's for quantities related between them by a mathematical function) Saturation vapor pressure of water (see Table F.3) Enhancement factor (see Table F.2) Shear modulus 269 Chapter 8 Symbols previously reported may be used in the present chapter, but are not listed here. F Ptr Ppr std. Ppgauge (Ptr - Ppr std.) (Pprstd. - Ptr) n Force due to the application of a pressure P to a pistoncylinder unit of effective area Ae (in first approximation F=pAe) Pressure reading of a transducer Pressure value measured by a primary standard Pressure value measured by a piston gauge Pressure calibration difference Pressure calibration correction Number of measurements Result of the ith measurement of the physical quantity x (i variable from 1 to n)

6 270 x p=/(x) x GF e R C f.s. LVDT List of Symbols Arithmetic mean of the n measurement results Interpolating equation of a transducer Output signal of a transducer, frequently corrected for its zero output value Gauge factor (GF = e dr/r for a strain gauge transducer) Strain Electrical resistance Electrical capacitance Full scale Linear variable differential transformer Chapter 9 Symbols previously reported may be used in the present chapter, but are not listed here. t.p. PIP TIP v.p. c.p. m.l. TIP (Hg) d= T- TIP (Hg) F Triple point Triple-point pressure Triple-point temperature Vapor pressure Critical point Melting line Mercury triple point ( K on ITS-90) Melted fraction (1/F= 1 is equivalent to 100% melted, i.e., liquidus point) Chapter 10 Symbols previously reported may be used in the present chapter, but are not listed here. Pc Pw Po = (Pc + Pw)/2 Tc Tw To=(Tc+ Tw)/2 d r A '1(T, p) Cold pressure Warm pressure Cold temperature Warm temperature Tube diameter Tube radius Mean free path orgas molecules Gas Viscosity at temperature T and pressure P

7 List of Symbols '1o(To, p) R' = (Tw/TJ1/2 R"=pw/Pc D tp g f "( NG Nw LJp c5(ljp) Gas viscosity at temperature To and pressure p Collisional diameter of a gas molecule Pressure shifting factor Momentum accommodation coefficient Geometry factor Number of gas-gas collisions Number of gas-surface collisions Thermomolecular pressure correction calculated on the basis of the Weber-Schmidt equation Difference between the Weber-Schmidt equation and experimental values of the thermomolecular pressure correction 271 Symbols used specifically in particular areas of application or used to define constants or calculation parameters are explained in the text.