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An Adiabatic Saturation Psychrometer

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An Adiabatic Saturation Psychrometer JOURNAL O F RESEAR CH 01 the Notionol Bureou of Standards - C. Engineering ond Instrumentation Vol. 72C, No.1 , Jonuary- Morch 1968 An Adiabatic Saturation Psychrometer Lewis Greenspan and Arnold Wexler Institute for Basic Standards, National Bureau of StandaFds, Washington, D.C. 20234 (November 17, 1967) An adiabatic satu ration psychromet e r for measuring the humidity of gases, as well as the vapor content of va por-gas mlXtures, IS descrIbed: The. In strument behaves in accordance with predictions d e du ~ e d solely fro m thermodyna mIc consIderatIO ns. With water-air, water-hydrogen, carbon tetra­ c hl o ~ld e - h y d roge n , carbon tetrachlonde-oxygen and tolue ne-air syste ms, at room te mperature, atmos­ pherI c pressure, and ~a s fl ow rates ?f 1.3 to 5.2 liters pe r minute, measured wet-bulb te mperatures agree WIth calc ul ated thermod yna mIc ~ e t-bul b tempera tures" to within the accuracy of the measure­ ments and the uncertamtles I~ the publIshed the rmodynamic data used in the computations. For the wate r-aIr syste m, the systema tI c and ra ndom errors due to these sources are estima ted at 0 027 deg C and 0.019 deg C r e~ p ec tiv e l y. The agreement between the cal cul ated and measured wet-bulb te mpera­ ture. IS 0.029 deg C, whle h a t a dry-bulb temperature of 25 °C and an ambient pressure of 1 bar is e qUlv ~ l e nt to a n uncertalllty In relative humidity which varies from 1/8 to 1/4 percent. The time con­ ~ tant IS a functIOn of the gas fl ow rate; at fl ow rates of 3_ 75 to 5_2 liters per minute, the time constant IS of the order of 3/4 mmute. Key Words: Adia bati c satu ration, gas mixtures, humidity, hyg rome te r, mixing ratio, moist gas, psychrometer, psychrometnc factor, saturation, thermod yna mic wet-bulb te mper a­ ture, vapor conte nt, wet-bulb. 1. Introduction yield results that are in nominal agreement with empirical facts for water vapor-air mixtures_ When The psychrometer is one of the oldest and most these formulas are applied to other vapor-gas mix­ common instruments for meas uring the humidity of tures, they fail to predict the correct vapor conte nt. moist air. In its elemental form it consists of two The wet-bulb thermometer of a psyc hrometer in a thermometers; the bulb of one is cov ered with a wic k steady-state condition experiences simultaneous heat and is moistened; the bulb of the other is left bare and and mass transfer. Although theories based on heat dry_ Evaporation of water from the moistened wick and mass transfer laws lead to equations which have a lowers its temperature below the ambient or dry-bulb structural similarity to those derived from thermo­ te mperature _ The wet-bulb temperature attained dynamic reasoning as well as to those of empirical with the conventional psychrometer is dependent origin, they also involve the ratio of thermal to mass on many factors in addition to the moisture and diffusivities [3 , 11- 21]. Even these equations which te mperature state of the gas [1-4).1 Although at­ yield results in closer agreement with experimental te mpts have been made to develop a theory that data, do not completely depict all psychrometric w0l!ld correctly interrelate the parameters affecting behavior. For the water-air system, the ratio of thermal the behavior of the conventional psychrometer there to mass diffusivity is close to one , accounting, in part, is no theory which completely describes it ~ per­ for the nominal agreement between the predictions formance_ In the well-known convection or adiabatic based on the convection theory with those based on saturation theory [5- 10], the principles of classical heat and mass transfer laws_ In general, this ratio thermodynamics exclusively are used to derive a is greater than one [11, 221- formula that predicts the humidity of a moist gas from It would be advantageous to have an adequate wet- and dry-bulb thermometer measurements_ Un­ theoretical basis for the behavior of the conventional fortunately the conventional psychrometer, even psychrometer, but lacking a rational theory which under steady-state conditions, is an open system accurately and fully describes the operation of the undergoing a nonequilibrium process which cannot conventional psychrometer, one can invert the prob­ be depicted completely by classical thermodynamic lem and inquire whether a psychrometer can be built theory. It is fortuitous that the formulas so derived which will behave in accordance with the postulates of classical thermodynamic s_ It appears that such a I Figures in brac kets indicate the literature references at the end of this paper. psychrometer can be designed and constructed and 28 3- 5760L-68-3 33 that its behavior can be predicted by thermodynamic h ~( P,Tw) =the enthalpy of 1 g of pure com­ reasoning and expressed in mathematical form. pressed liquid (or solid) of the vapor component at pressure P and tem­ perature Tw; 2. Theoretical Considerations he?, Tw, rw) =the enthalpy of (l+rw) g of gas mix­ ture saturated with respect to the Consider a closed system undergoing an isobaric second or vapor component at pres­ quasi-static process in which compressed liquid sure ? and saturation temperature (or solid) at pressure P and temperature Tw is intro­ Tw, that is, the enthalpy of a gas mix­ duced into a gas at pressure P, temperature T, and ture containing one gram of vapor-free mixing rati0 2 r to bring the gas adiabatically to satura­ gas and rw g of the vapor component; tion at pressure P, temperature Tw , and mixing ratio and rw. The term "gas" as used here and elsewhere in rw=rw(P, Tw)=the mass of vapor component of the this paper is intended to include a gaseous mixture gas mixture per unit mass of vapor­ of which one constituent or component is a permanent free gas of the mixture when it is gas or mixture of permanent gases and the second saturated with respect to the vapor constitutent or component is the vapor of the com­ component at pressure ? and tem­ pressed liquid involved in the psychrometric process perature Tw. and manifests itself as a product of evaporation. Since The "thermodynamic wet-bulb temperature" is the process is adiabatic and isobaric the sum of the defined [23] as the solution for Twin eq (1). enthalpies of the various phases within the system In order to facilitate the mathematical development are conserved, thus the initial and final enthalpies we introduce the following additional notation: are equal, leading to the following equation: t1T= (T- Tw) = The wet-bulb depression; h(P, T , r) = h(P, Tw, rw) - (rw - r) . h ~( P, Tw) (1) h(P, Tw, r)=the enthalpy of O+r) g of gas mixture at pressure?, temperature Tw where (the same as the "thermodynamic wet-bulb temperature" of the original h(P, T, r)=The enthalpy of (l+r) g of gas gas mixture), and mixing ratio r (the mixture at pressure P, temperature T same as the mixing ratio of the origi­ and mixing ratio r, that is, the en­ nal gas mixture); thalpy of a mixture consisting on 1 g h(P, T , 0) = h(P, T, r= 0) = the enthalpy of 1 g of of the vapor-free gas and r g of the the pure first (vapor-free) component vapor component; of the mixture at pressure P and r= the mass of vapor in the original gas temperature T;·· and mixture per unit mass of vapor-free h(P, Tw, 0) = h(P, Tw, r= 0) = the enthalpy ofl g of gas with which the vapor is associated; the pure first component of the mix­ ture at pressure P and temperature 2ln several of the engin eerin g disciplines r is call ed the humidity ratio. Tw . Let F=F(?, T , Tw, r) = [he?, T , r) -he?, Tw, r)] (2) and C. - [h(P, T , 0) -h(P, Tw, 0)] p,m- (T-Tw) (3) where Cp = the specific heat at constant pressure of the pure vapor-free component. Also let C = [he?, T, r) -he?, Tw, r)] - [h(P, T , 0) -he?, Tw, 0)] pV,m r(T-Tw) (4) and L = [h(P, Tw, rw) -h(P, Tw, r) - (rw-r)h~(? , Tw)] (5) V,T . (rw- r) 34 From the above definition, it will be clear that B = C/lV , III /Lv, r (10) C" , II/ represents the mean specific heat at constant pressure of the pure vapor-free first component over substituting these in eq (8), and solving it for r, one the temperature range from Tw to T. The entity Cpv, 11/ finds may be interpreted as the "effe ctive" specific heat at constant pressure P of the vapor component of the A6.T mixture taken as a mean over a temperature range (11) [1 + B6.11 from Tw to T and at a mixing ratio of r. Finally, Lv, r may be understood as the "effective" latent heat of where 6.T= T- Tw. vaporization (or sublimation) of the vapor component Solving eq (11) for A one obtains of the mixture at constant pressure P and constant te mperature Tw. It will be seen that Lv, r is taken as a mean while (rw-r) gram of vapor component A (12) evaporates into the gas mixture from a plane surface of its liquid phase per gram of first component.
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