Critical Region Thermodynamic Properties of D2O in the

Thermodynamic Properties of D2O in the Critical Region

Cite as: Journal of Physical and Chemical Reference Data 12, 513 (1983); Published Online: 15 October 2009 B. Kamgar-Parsi, J. M. H. Levelt Sengers, and J. V. Sengers

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Journal of Physical and Chemical Reference Data 12, 513 (1983); ? 1983 American Institute of Physics for the National Institute of Standards and Technology.

12, 513

thermodynamic Properties of 020 in the Critical Region

B. Kamgar-Parsi Institute/or Physical Science and Technology, University 0/Maryland, College Park, Maryland 20742

J. M. H. Levelt Sengers

Thermophysics Division, National Bureau ofStandards, Washington, DC 20234

and

J. V. Sengers

Institute/or PhysicalScience and Technology, Universityo/Maryland, College Park. Maryland 20742 and Thermophysics Division, National

.

Bureau 0/Standards, Washington, DC20234

An analysis is presented ofthe thermodynaJ1lic propedies .ofD 20 iu the c.a-itkall?egiull. It is shown that the data can be represented by the same revised and? extended scaled

fundamental equation formulated earlier for the thermodynamic' properties of H 20 in critical region. The equation is valid in the range 220-465 kglm3 in density and 638-683 K

in temperature. Tabulated values ofthe thermodynamic properties of D20 in the critical region are presented. A comparison with a comprehensive analytic fundamental equation,

recently formulated?by Hill and co-workers, is included in the paper.

~ey_~ords: critical ~ameters' critical region;~IJer..gy;_rnthJUp-Y~ntmp-y~uati01Lof.state;JleaYY_ steam; heavy water; sound velocity; specific heat; thermodynamic properties; critically evaluated data.

Contents

Page

1. Introduction ........................................................ . 513 2. Fundamental Equation ........................................ 513 3. Data Sources ........................................................ 514 4. Critical.Point Parameters ...............................,..... 515 5.. Equation ofState.................................................. 516 6.. Specific Heat~........................................................ 517 7. Comparison with Equation of Hill et al............... 519 8. Thermodynamic Tables ....................................... 520 Acknowled.gments .................................................... . 520 References ................................................................. 520

Page

Appendix A: Definition of Scaled Fundamental Equation for the Critical Region....~.......................... 520

Appendix B: Parameters for the Thermodynamic

Surfa~e of D 20 ill tht:: Criti"",l Region ...................... 521

Appendix C: Tables of Thermodynamic Properties of D20 in the Critical Region ................................... 521 Appendix D: Computer Program for Table Generation ........?........................................?..................?..... 528

Appendix E: Units and Conversion Factors ........... 529

1. Introduction

The modem theory ofcritical phenomena predicts that the singular behavior of the thermodynamic properties of Ouids in the vicinity ofthe critical point satisfies scaling laws with universal critical exponents and scaling functions. 1,2 A revised and extended scaled fundamental equation that incorporates the theoretical predictions for the asymptotic critical behavior was earlierformulated and shown to represent the thermodynamic properties of H20 in the critical region.3 In this paper WfHlse the s.9me fundament.n1equation to analyze and represent the available experimental information for D20 in the critical region. We present detailed com-

@ 1983 by the u.s. Secretary of Commerce on behalf of the United States. This copyright is assigned to the American Institute of Physics and the American Chemical Society. Reprints available from ACS; see Reprint List at back of issue.

parisons ofthe scaled fundamental equation with the experi-

mental data and give tabulated?values, derived from our

fundamental equation, for the pressure, energy, enthalpy,

entropy, specific heats at constant pressure and at constant

volume, and velocity of sound.

A global fundamental equation for the thermodynamic

properties ofD;zO, which is analytic at the critical point~ wag

recently formulated by Hill, MacMillan, and Lee.4 We in-

clude also?a comparison between ournonanalytic fundamen-

tal equation and the analytic fundamental equation ofHill et

al.

.

2. Fundamental E.quation

Our fundamental equation involves a relationship between the intensive thermodynamic variables pressure P, chemical potential 1-?, and temperature T. Specifically w~

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513

J. Phys. Chem. Ref. Data, Vol. 12, No.3, 1983

514

KAMGAR-PARSI, LEVELT SENGERS, AND SENGERS

consider the reduced variables

- r ' - P Tc

p= T'P'

P__-Yp :P'cpTc-'

T=

Tc

)

(1

c

. c

where Pc is the critical pressure, Tc the critical temperature,

andpc the critical density. Th~.fundamental equation ~ields

the thermodynamic potential P as a function of{.t and T and

has the form

P = fiT) + A{.t + i\ iA{uft + AP,

(2)

with

A{.t = fl- fliT).

(4)

.Here Po(T) and{.to(T) are analYtic functions ofAT, while AP

contains the singular, i.e., nonanalytic, contributions to the

potential P. The equations for these functions are fully speci-

fied in Appendix A. The analytic functions are represented

by truncated power series in terms ofAT, while the singular

part AI' is related to A{.t and ATwith the aid oftwo auxiliary

(parametric) variables rand O.

.

The fundamental equation contains the following con-

stants: Three critical parameters Pc , Tc'Pc which specify the

reduced variables defined in Eq. (2.1), three critical expo-

nents 13, 8, AI' and five parameters a, ko, kIt C, b 2 in the singular contribution AP, four background paramete!s PI'

_7:2' P3, 1'11 th!! specify the anal~ic contributi~n~_to P as a

function ofA Tand Afl, and four background parameters fle'

PI' flz, fl3 that specify the analytic contributions to the ca-

loric properties as a function of temperatu~. The critical

exponents /3, 8, A 1 and the parameter b 2 in AP are universal,

i.e., independent of the nature of the fluid; hence, for 0 20 they have the same values as previously adopted for 1:!:zO.3

The coefficlents a, ko, k l , and c in the equations for J.P are

adjustable amplitudes that depend in principle on the nature

of the fluid; however we find that for 0,,0 these coefficients

have, within currently available experimental accuracy, 'the

same values as found for H 20. Hence the only constants for

D20 that differ from those for H20 are the critical para~

etersPc ' Tc,Pc and the analytic background pan),metersPI ,

Pi, 1'3' 1'11 and Pc ,PI' ji,2' ji,3 for the pressure and the caloric

properties. The values of the constants in this fundamental equa-

tion for D 20 are listed in Appendix B. The equation is valid in a range of temperatures and densities bounded by

638 K,T,683 K,

(5) 220 kg/m3 ................
................

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