Principle of Corresponding States

[Ángel Martin]

Principle of Corresponding States. [MARTIN]
From the author’s Engineering Collection, included in the ETSII3 module


This program evaluates the third of the {P,V,T} properties in the superheated vapor region of a non-perfect gas when the other two are known. It uses the Principle of Corresponding States (PCS) with a modification of the equation of state proposed by Joseph Martin, expressed in reduced form and cubic in the volume; and given by the expression:

Pr = Tr / [Zc.Vr – B ] – A / { Tr^n [ Zc.Vr – B + 1/8 ]^2 }

The Critical constants {Tc, Pc, Vc} are widely available in the technical reference data banks. Zc is the experimental compressibility factor, typically smaller than the theoretical one (Zt = Pc.Vc/R.Tc). The constants {A, B, n} are non-dimensional (“n” is not the number of moles) and specific to each substance. They are obtained using semi-empirical methods, which description is beyond the scope of this manual. Approximate values for A, B can be taken as A = 27/64, and: B = 0.72.Zc – 0.152

The table below shows the values for a few gases that you can use to check the program.

Code:

           R-40      R-50      R-170     R-290     R-764      R-744
Parameter  CH3Cl     CH4       C2H6      C3H8      SO2        CO2
---------------------------------------------------------------------------------------
Zc         0.268     0.291     0.27844   0.2701    0.268      0.274
A          0.421875  0.421875  0.421875  0.421875  0.421875   0.421875
B          0.0495    0.0575    0.05739   0.0511    0.051      0.0453
n          0.85      0.75      0.45      0.40      0.50       0.50
Tc (C)     143.1     -82.3     32.0908   96.85     157.19     30.978
Pc (kp/cm2)68.0997   97.6104   50.3      43.4      80.2996    75.2245
Vc (cm3/g) 2.7027    6.200     4.7619    4.4248    1.9084     2.1359
PM (g/mol) 50.491    16.044    30.07     44.09     64.06      44.01

The programs work internally with the units reflected in the table but you can input and output the values in any other units. It comes without saying that these programs make extensive use of the Unit Management System (UMS), therefore the unit Conversion Module needs to be plugged into the calculator.

This program provides a subset of the functionality of the Thermodynamic Properties of Refrigerants, to be described in the next section. Here the three magnitudes are treated in an interchangeable solutions form – so you can enter with any two of them known to obtain the third.

• The specific volume is the largest (real) root of the cubic equation in V, obtained by the auxiliary routine “ROOT3”, included in the module.
• Calculation of the temperature requires the root-finding routine “SLV”, also included in the module (no additional dependencies).

Examples.

Calculate the specific volume of CO2 in the saturated region knowing its Martin constants and critical value as per the table above. The initial conditions point data are T = 0 deg C, and P = 35.4861 kp/cm2. Check the result obtained using it as data point for a reversed calculation of P (with same T) and T (with same P).

Result: Ve = 0.0105 m3/kg

Feeding this result as initial input:

P (Ve; 125 C) = 35,4861 kp/kg
T (Ve; 50.9825 kp/cm2) = 2,0000E-7 deg C