Dieterici equation

II] Dieterici equation Dieterici introduced an exponential factor to account for the effect of molecular attraction on the pressure. His equation is given by,... 

Dieterici s equation A modification of van der Waals equation, in which account is taken of the pressure gradient at the boundary of the gas. It is written... 

The need for so many constants shews, says Weinstein (Tliermodynamik u. Kinetik der Korper, I., 869), how really unsatisfactory is yet the condition of this branch of enquiry. Dieterici (1899) proposed to replace r2 in van der Waals equation by ... 

Dieterici (1895) has observed that this ratio would not be less than 8 if b were assumed to be a function of the volume on the assumption of the constancy of h he has given two new equations of state which give values of b/el closely approximating to the observed numbers... 

If we take Dieterici s numbers for the vapour pressures, and Roloff s for the freezing-points, of solutions of potassium chloride, we can calculate the osmotic pressure (P0) from the two equations ... 

The Dieterici equation is one that effectively represents the (p, Vm, T) properties of gases under certain conditions. It has the form... 

Figure A3.3 compares the experimental (corresponding states) results with the predictions from the van der Waals. modified Berthelot, Dieterici, and Redlich-Kwong equations of state.b The comparison is not so direct for the Soave and Peng-Robinson equations of state, since the reduced equation still includes to, the acentric factor. Figure A3.4 compares the corresponding states line, with the prediction from the Soave equation, using four different values of to. The acentric factors chosen are those for H (o> = —0.218), CH4 (to = 0.011),...

Figure A3.3 Comparison of the experimental r (dashed lines) with the c values calculated from the (a) van der Waals, (b) modified Berthelot, (c) Dieterici, and (d) Redlich-Kwong equations of state expressed in reduced form.

The Dieterici equation works well near the critical region, but it deviates significantly at higher reduced temperatures. 

After the qualitative success of the van der Waals equation in explaining the properties of real gases, people noticed that it is not always accurate and so sought improvements. Dieterici came up with the formulation... 

In conclusion, it may be said that van der Waals equations can only provide reasonably accurate representation over limited ranges of variation of the pressure and temperature. For this reason many attempts were made to produce a more satisfactory equation by modifying vanderWaals equations. Such modifications were made by Berthelot (See item b ), Callendar (See item c-2), Clausius (See item C3), Dieterici (See item d2), Hirschfelder et al (See item 113), Keyes (See item ki), Lees (See item I3), and Macleod (See item mi) Accdg to Dunkle (Ref 17), for high temps and moderate pressures which give rise to large values of V so that P55>a/v2, van der Waals equation reduces to Abel s equation (See item ai)... 

Erpenbeck Miller (Addnl Ref I) stated that the Dieterici equation better represents the fluid properties near the liquid region and it gives a value RTc/pcvc =3.69, nearly the average for all common gases. Subscript c means critical. Same value is given by Joffe (Ref 2b, p 1216) for eqs (1)... 

Dunkle s Syllabus (I96O-I96I), p 15d (Addnl information on Virial equation of state) p 15d (Macleod Dieterici equations of state) 13a) 8thSympCombstn(1962) - papers and pages are indicated in the text 14) lOthSympCombstn... 

H) W. Fickett W.W. Wood, The Physics of Fluids 1 (6), 528-34 (Nov-Dec 1958) (Detonation-product equations of state, known as "constant-/ and "constant-)/ , obtained from hydrodynamic data) I) J.J. Erpenbeck D.G. Miller, IEC 51, 329-31 (March 1959) (Semiempirical vapor pressure relation based on Dieterici s equation of state J) K.A. Kobe P.S. Murti, IEC 51, 332 (March 1959) (Ideal critical volumes for generalized correlations) (Application to the Macleod equation of state) Kj) S. Katz et al, jApplPhys 10, 568-76(April 1959) (Hugoniot equation of state of aluminum and steel) K2) S.J. Jacobs, jAmRocketSoc 30, 151(1960) (Review of semi-empirical equations of state)... 

Other empirical gas laws exist (Berthelot,35 Dieterici,36 Beattie37-Bridgman,38 etc.), but the search for a simple, yet generally valid, gas law for all gases at all conditions of temperature, pressure, and volume has failed. Engineers must thus rely on tabular data (e.g., steam tables) rather than on a master equation. One intuitively useful gas equation is Kamerlingh Onnes 39 virial equation (a fancy term for a power series) ... 

The value (Cp - C ) calculated on the Dieterici equation is very complicated and need not be given here... 

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