The difficulties of realizing a temperature of 0.000 °C in an ice bath are substantial. The ice point is defined at the temperature of melting pure ice in contact with water which is saturated with air. Pure water is in equilibrium with pure ice at atmospheric pressure and a temperature of 0.003 °C. This temperature difference corresponds to 2.1 mm of mercury at the CO point. Since freshly melted ice is free of air, the conditions of the definition are hard to realize. The investigators both at MIT and the NBS were fully aware of these difficulties and it is probable that their temperatures did not differ by more than 0.0005 °C. Apparently, at least part of the difference between the values published by the two laboratories must be charged to the preparation of the samples of carbon dioxide. Both laboratories took elaborate precautions to avoid chemical contamination. The gas was obtained by decomposition of sodium bicarbonate, dried with P20%, and then sublimed five to eight times. In addition, at the NBS, the liquid was cooled by evaporation several times to obtain the solid. While substantial amounts of chemical contaminants seem unlikely, the possibility of isotope separation cannot be ruled out. Recent determinations of the CO2 point, including those made in Europe [4, 6], are lower than this measurement by an amount which slightly exceeds the sum of the uncertainties estimated by the various authors. This difference may be systematic as between the static and dynamic methods. However, one point with regard to the gas-lubricated piston gage should be mentioned. Carbon dioxide cools substantially on expansion. If this cooling reduces the temperature of the piston significantly, the effective area would be decreased and the apparent pressure increased. Estimates based on the Joule-Thompson coefficient and thermal conductivity of CO2, the rate of leak, and the clearance indicate that this effect would not exceed 0.1 deg in temperature or 2 ppm in the pressure. This point could be verified by operation of the piston gage with helium, which has a positive Joule-Thompson coefficient.

5. Conclusions

In the use of the vapor pressure of CO2 as a means of calibration, at least three factors are of comparable

importance, Le.. pressure measurement, temperatu measurement, and preparation of the sample.

Measurement of the vapor pressure of CO2 by t dynamic method appears to be insensitive to impu ties, at least at the level found in commerically av abie CO, in gas cylinders. The use of a gas-lubricat piston gage eliminates the need of fluid or diaphra, separators with the associated possible systema errors.

The authors are indebted to J. L. Cross and associates who furnished the piston gage and temp ture measuring equipment and determined t parameters.

6. References

[1] O. C. Bridgeman, A fixed point for the calibration of pre gages. The vapor pressure of liquid carbon dioxide at J. Amer. Chem. Soc., 49, 1174-1183 May 1927). [2] C. H. Meyers and M. S. Van Dusen. The vapor pressu liquid and solid carbon dioxide, J. Res. NBS 10, 381 | RP538.

[3] J. R. Roebuck and Winston Cram. A multiple column me manometer for pressure to 200 atmospheres, Rev. of Instr.. 8, 215 (1937)L

[4] A. Michels, et al., The vapor pressure of liquid carbon di J. Appl. Phys. 16, 501 (1950)

[5] W. C. Edmister, H. G. McMath, and R. C. Lee, Pressure parisons for dead weight piston gages and vapor pre of carbon dioxide, Oklahoma State University, unpub paper (1964).

[6] R. G. P. Greig and R. S. Dadson. The vapour pressure of c dioxide at 0.01 °C. Brit. J. Appl. Phys., 17, 1633 (1966 [7] H. F. Stimson, Precision resistance thermometry and points, precision measurement and calibration, II, He mechanics, NBS Handbook 77, 40 (1964).

[8] E. C. Lloyd and D. P. Johnson. Static and dynamic calibr of pressure-measuring instruments at the National E of Standards, Automatic and remote control, p. 274 (Pr ings of the First International Congress of the Intern Federation for Automatic Control, Moscow) (Buttery London, 1960).

[9] D. P. Johnson and D. H. Newhall, The piston gage as a pressure-measuring instrument, Trans. ASME, 75, 301 [10] J. L. Cross, Reduction of Data for piston gage pressure urements, NBS Mono. 65 (1963).

[11] J. Hilsenrath et al., OMNITAB, a computer program for tical and numerical analysis, NBS Handbook 101 (196

(Paper 72C1

1. Introduction

The psychrometer is one of the oldest and most common instruments for measuring the humidity of moist air. In its elemental form it consists of two thermometers; the bulb of one is covered with a wick and is moistened; the bulb of the other is left bare and dry. Evaporation of water from the moistened wick lowers its temperature below the ambient or dry-bulb temperature. The wet-bulb temperature attained with the conventional psychrometer is dependent on many factors in addition to the moisture and temperature state of the gas [1-4]. Although attempts have been made to develop a theory that would correctly interrelate the parameters affecting the behavior of the conventional psychrometer, there no theory which completely describes its performance. In the well-known convection or adiabatic saturation theory [5-10], the principles of classical thermodynamics exclusively are used to derive a formula that predicts the humidity of a moist gas from wet and dry-bulb thermometer measurements. Unfortunately the conventional psychrometer, even under steady-state conditions, is an open system undergoing a nonequilibrium process which cannot be depicted completely by classical thermodynamic theory. It is fortuitous that the formulas so derived

* Figures in brackets indicate the literature references at the end of this paper.

yield results that are in nominal agreement with empirical facts for water vapor-air mixtures. When these formulas are applied to other vapor-gas mixtures, they fail to predict the correct vapor content. The wet-bulb thermometer of a psychrometer in a steady-state condition experiences simultaneous heat and mass transfer. Although theories based on heat and mass transfer laws lead to equations which have a structural similarity to those derived from thermodynamic reasoning as well as to those of empirical origin, they also involve the ratio of thermal to mass diffusivities [3, 11-21]. Even these equations, which yield results in closer agreement with experimental data, do not completely depict all psychrometric behavior. For the water-air system, the ratio of thermal to mass diffusivity is close to one, accounting, in part, for the nominal agreement between the predictions based on the convection theory with those based on heat and mass transfer laws. In general, this ratio is greater than one [11, 22].

It would be advantageous to have an adequate theoretical basis for the behavior of the conventional psychrometer, but lacking a rational theory which accurately and fully describes the operation of the conventional psychrometer, one can invert the problem and inquire whether a psychrometer can be built which will behave in accordance with the postulates of classical thermodynamics. It appears that such a psychrometer can be designed and constructed and

that its behavior can be predicted by thermodynamic reasoning and expressed in mathematical form.

2. Theoretical Considerations

66

Consider a closed system undergoing an isobaric quasi-static process in which compressed liquid (or solid) at pressure P and temperature Tu is introduced into a gas at pressure P, temperature T, and mixing ratio2r to bring the gas adiabatically to saturation at pressure P, temperature Tw, and mixing ratio Tw. The term 'gas" as used here and elsewhere in this paper is intended to include a gaseous mixture of which one constituent or component is a permanent gas or mixture of permanent gases and the second constitutent or component is the vapor of the compressed liquid involved in the psychrometric process and manifests itself as a product of evaporation. Since the process is adiabatic and isobaric the sum of the enthalpies of the various phases within the system. are conserved, thus the initial and final enthalpies are equal, leading to the following equation:

h(P, T, r) = h(P, Tw, гw) — (гw − r) · h' (P, Tw) (1) where

h(P, T, r) = The enthalpy of (1+r) g of gas mixture at pressure P, temperature T and mixing ratio r, that is, the enthalpy of a mixture consisting on 1 g of the vapor-free gas and r g of the vapor component;

r = the mass of vapor in the original gas mixture per unit mass of vapor-free gas with which the vapor is associated;

2 In several of the engineering disciplines r is called the humidity ratio.

AT= (T-Tw) = The wet-bulb depression; h(P, Tw, r) = the enthalpy of (1+r) g of gas mixture at pressure P, temperature Tr (the same as the "thermodynamic wet-bulb temperature" of the original gas mixture), and mixing ratio r (the same as the mixing ratio of the origi nal gas mixture);

h(P, T, 0) = h(P, T, r=0) = the enthalpy of 1 g of the pure first (vapor-free) component of the mixture at pressure P and temperature T; and

h(P, Tw, 0) = h(P, Tw, r=0)= the enthalpy of 1 g of the pure first component of the mixture at pressure P and temperature Tw

Also let

=

(3)

(4)

(5)

r

From the above definition, it will be clear that Cp. m represents the mean specific heat at constant pressure of the pure vapor-free first component over the temperature range from Tw to T. The entity Cpv, may be interpreted as the "effective" specific heat at constant pressure P of the vapor component of the mixture taken as a mean over a temperature range from T to T and at a mixing ratio of r. Finally, L., may be understood as the "effective" latent heat of vaporization (or sublimation) of the vapor component of the mixture at constant pressure P and constant temperature Tw. It will be seen that Lv, r is taken as a mean while (rw-r) gram of vapor component evaporates into the gas mixture from a plane surface of its liquid phase per gram of first component. Both mixture and liquid must be at the same pressure P and temperature Tw, the gas mixture having a mixing ratior initially and attaining a mixing ratio u finally as a result of the process of evaporation.

It should be noted that the "effective" specific heat Cpt, m and the "effective" latent heat of vaporization Lr.r both differ from their counterparts pertinent to the pure phase of the second (vapor) component owing to the interactions between the molecules of the first and second components of the gas mixture, and due to other small effects [24].

By adding to the function F each of the quantities h(P, T, 0) and h(P, Tw, 0), both with positive and negative signs, respectively, one obtains the useful identity

F=[h(P, T, r)-h(P, Tw, r)]

= [h (P, T, r) — h(P, T, 0)]–[h(P, Tw, r) − h (P, Tw, 0)] +[h(P, T, 0)-h(P, Tw, 0)]. (6)

When one subtracts h(P, Tw, r) from both the left-hand and right-hand members of eq (1), it is obvious that the left-hand member transforms to the function F. Therefore, the right-hand member of eq (1) minus h(P, Tu, r) is also equal to F, so that we can equate this difference to eq (6) which yields the relationship

[h(P, Tw, w)-h(P, Tw, r)] — (гw− r)h'(P, Tw)

=[h(P, T, r)-h(P, T, 0)]

-[h(P, Tw, r)-h(P, Tw, 0)]

(14)

e=

ew (P-e) (1+B'AT) (P-ew)

(P-e) AoAT (1+ B'AT)

(15)

(16)

Ao

My L

e = the partial pressure of the vapor component in the original gas mixture;

ew=the saturation vapor pressure of the liquid phase of the vapor component at temperature Tu P the total pressure;

C=the pure phase specific heat of the vapor at constant pressure;

L= the pure phase latent heat of vaporization of the vapor:

C= the specific heat of the vapor-free gas at constant pressure;

which is identical to the classical equation often used to represent the behavior of the conventional psychrometer.

It does not appear feasible to construct a practical psychrometer that is an embodiment of a closed system undergoing the ideal adiabatic isobaric saturation process which serves as the basis of eq (1). On the other hand, an open system undergoing a steady-flow process would appear to be operationally feasible, and such a system was constructed and its performance investigated. The aim was to approach ideal conditions as closely as practical, namely to bring compressed liquid (or solid) to pressure P and temperature Te, to evaporate it into a gas stream at pressure P, temperature T and mixing ratio r, and to bring the gas adiabatically to saturation at pressure P, temperature Tw and mixing ratio r. This system then becomes an adiabatic saturator operating at constant pressure. If nothing enters to violate the conditions of eq (1), the adiabatic saturator becomes an "adiabatic saturation psychrometer" since measured values of P, T, and Tw can be inserted into eq (11) to obtain the mixing ratio of the entrant gas stream. It was realized that practical and theoretical matters, such as heat exchanges due to radiation and conduction, and pressure drop associated with flow, would be among the factors limiting the possibility of attaining the ideal, especially in view of the desire to keep the apparatus simple for ease of construction. It was left, therefore, to experiment to serve as the indicator of how close the actual psychrometer conformed to theory.

3. Background

In 1922, W. K. Lewis performed several experiments in which a dried gas was bubbled through a volatile liquid in a Dewar flask containing glass beads, the gas being discharged into the liquid through a vacuumjacketed glass inlet tube. For water-air, water-carbon dioxide, toluol-air and chlorbenzol-air the gas substantially became saturated and the liquid (as well as the effluent gas) eventually reached a steady-state temperature that was essentially the "thermodynamic wet-bulb temperature." The readings of wet-bulb temperature in the experiments using water, toluol and chlorbenzol as the liquid were independent of air velocity and of the amount of air contact with the liquid. This was not the case in the experiments with

liquids of higher vapor pressure. The discrepa probably was due to incomplete saturation and inc plete heat transfer between the gas and liquid ra than lack of constancy of the wet-bulb temperatur Lewis assumed.

Nanda and Kapur [28] performed similar ex ments, bubbling dried air into a Dewar containing: liquids as acetone, methyl alcohol, ethyl alcohol, butyl alcohol. After a considerable length of time liquid temperature approached the "thermodyn. wet-bulb temperature.'

We also repeated these experiments, and in c so found it necessary to use a vacuum-jacketed inlet tube, such as Lewis had used, for bubblin gas through the liquid in the Dewar flask. With inlet tube, which reduced precooling of the inle prior to discharge into the liquid, steady-state peratures of the liquids were obtained, which in close agreement with calculated "thermodyn wet-bulb temperatures," provided the gas flow very low and only after extended continuous usually hours.

Although "thermodynamic wet-bulb temperati could be obtained with the Dewar flask, the lov flow rates, and the extremely long time necessa reach steady-state conditions at these flow 1 seemed to preclude its use as a practical instru for measuring humidity.

Carrier and Lindsay [25], and Dropkin [14] structed large scale, engineering-type apparatu obtaining adiabatic saturation. The essential fe of these devices was the provision for passir over surfaces moistened with water that had precooled to, or close to, the wet-bulb temper within well-insulated ducts. The experiments formed by these investigators were limited t water-air system.

In 1961, J. D. Wentzel described a psychro which apparently measured the "thermody wet-bulb temperature" of water-air with hig curacy [29]. In his instrument, Wentzel atte to saturate adiabatically a stream of test air ( humidity was to be measured) with water vap fashion that appeared to approach the idealized s flow adiabatic process. Basically his instrumen sisted of a vacuum-insulated glass tube, the walls of which were silvered to reduce radiation e The tube was partially filled with a moistened 1 sponge through which the air flowed. Makeup was added intermittantly, in one design, an tinuously in a second design. In the latter versi continuous flow of makeup water was precoo an essentially equivalent instrument through part of the gas stream was channeled. To pr the possibility of drying of the sponge, excess n liquid was used. Wet-bulb temperatures were ured with thermocouples imbedded in the mo sponge. Wet-bulb temperature measuremer the water-air system corresponded very clo thermodynamic wet-bulb temperatures. known, however, that the wet-bulb temperat moist air as measured with a conventional psy

It