dc51bf9c-5d91-4483-895d-2b2e06c4b607 102 Alvaro Diaz Falconi 4 5 false false 0 10 decimal

Mixing gases

"Exact" value (Viacheslav maple's calculus)

Data

P 1 atm * :

T 300 K * :

Fluids Helium Xenon stack :

ν Fluids length :

ρ'.o 2.231 kg m 3^/ * :

x 0.6 0.4 stack mol mol / * :

x sum 1

Props

Mix :

k 1 ν range Mix Mix & Fluids k el [x k el var2str] concat : for

Mix Mix 2 substr : Helium[0.6]&Xenon[0.4]

D T T P P Mix CoolProp_Props #

lastError Initialize failed for backend: "?", fluid: "Helium&Xenon" fractions "[ 0.6000000000, 0.4000000000 ]"; error: Could not match the binary pair [7440-59-7,7440-63-3] - for now this is an error. : PropsSI("D","T",300,"P",101325,"Helium[0.6]&Xenon[0.4]")

ρ D T T P P Fluids CoolProp_Props vectorize : kg m 3^/ 0.1625 5.3612 21 mat

Tc TCRIT Fluids CoolProp_Props1 vectorize : K 5.1953 289.733 21 mat

Pc PCRIT Fluids CoolProp_Props1 vectorize : MPa 0.2276 5.842 21 mat

Notation:
prime is for the mixture

M M Fluids CoolProp_Props1 vectorize : g mol / 4.0026 131.293 21 mat

M' x k el M k el * k 1 ν sum : g mol / 54.9188

Method 1: As ideal gases

From

P V * n R * T * ≡

ρ m V / ≡

m MM n * ≡

ρ' M' P R.m T * / * : 2.230907 kg m 3^/ *

err ρ'.o ρ' - ρ'.o / abs : % 0.0042

Method 2: Using mixing density formula

Mole to mass fractions

y x M * vectorize M' / : 0.04372934 0.95627066 21 mat

ρ' 1 y k el ρ k el / k 1 ν sum / : 2.234906 kg m 3^/ *

err ρ'.o ρ' - ρ'.o / abs : % 0.1751

Method 3: Using Redlich-Kwong formula

b 23 nthroot 1 - 3 / mol K * J / * R.m 2^* Tc Pc / * vectorize : L mol / 0.1367 0.297 21 mat

volume constant correction for each compound

b' x k el b k el * k 1 ν sum : L mol / 0.2009

volume constant correction for the mixture. Notice that it is lineal in x

a 1923 nthroot 1 - (* / R.m 2^* Tc 2.5^Pc / * vectorize : J 2^K sqrt * mol 2^Pa * / 0.008 7.228 21 mat

attractive potential of molecules coefficient for each compound

k 1 ν range j 1 ν range α k j el a k el a j el * sqrt : for for

α J 2^K sqrt * mol 2^Pa * / 0.008 0.2403 0.2403 7.228 22 mat

The "a" coefficient for the mixture is not lineal in x, assuming that α(i,j) is the geometric mean of a(i) & a(j)

a' x k el x j el * α k j el * j 1 ν sum k 1 ν sum : J 2^K sqrt * mol 2^Pa * / 1.2747

attractive potential of molecules coefficient for the mixture

Now we can solve the Redlich-Kwong for the mixture like it was a compound

v' P R.m T * v' b' - / a' T sqrt v' * v' b' + (* / - ≡ v' 1 L mol / * ≡ FindRoot :

v' L mol / 24.7893

ρ' M' v' / : 2.2154 kg m 3^/ *

err ρ'.o ρ' - ρ'.o / abs : % 0.6981

Alvaro

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