Thermophysical Data and Scientific Constants
Introduction
The ThermophysicalData package
introduces the Chemicals subpackage, which gives the properties of an additional 2000 chemical species
and updates the CoolProp fluid properties engine to version 6.1
Additionally, the non-derived physical constants in the ScientificConstants package are updated to reflect those in the 2014 release of the CODATA Recommended Values of the Fundamental Physical Constants.
New Thermodynamic Data
Maple 2018 introduces the Chemicals subpackage. This uses a new data source* to give the thermodynamic properties of over 2000 gases, liquid and crystalline species.
* Bonnie J. McBride, Michael J. Zehe, and Sanford Gordon. NASA Glenn Coefficients for Calculating Thermodynamic Properties of Individual Species; 2002; https://www.grc.nasa.gov/WWW/CEAWeb/TP-2002-21556.htm.
The data can be used to study
chemical equilibrium composition
reaction constants and spontaneity
rocket performance
flame temperatures
explosion and detonation pressures
and many more applications
restart:withThermophysicalData
Chemicals,CoolProp,PHTChart,Property,PsychrometricChart,TemperatureEntropyChart
Heat of formation and molar mass of gaseous CO2
Chemicals:-PropertyHeatOfFormation,CO2(g),useunits;Chemicals:-PropertyMolarMass,CO2(g),useunits;
−393.51×103Jmol
44.01gmol
Enthalpy and entropy of gaseous CO2 at 300 K
Chemicals:-PropertyHmolar,CO2(g),temperature=300 K;Chemicals:-PropertySmolar,CO2(g),temperature=300 K;
−393.44×103Jmol
214.02JmolK
See help for more detail, including a list of the species.
Application: Adiabatic Flame Temperature of Butane
Liquid butane is burnt with 100% theoretical air at an initial temperature of 298.15 K. The combustion reaction is
C4H10 (l) + 6.5 O2 (g)+ 24.44 N2 (g) → 4 CO2 (g) + 5 H2O (g) + 24.44 N2 (g)
Here, we will calculate the adiabatic flame temperature of the combustion products.
Heat of formation of butane
h_f_C4H10≔Chemicals:-PropertyHeatOfFormation,C4H10(l),n-buta,useunits
−150.66kJmol
Enthalpies of the combustion products at a temperature T
h_N2≔Chemicals:-PropertyHmolar,N2(g),temperature=T:h_O2≔Chemicals:-PropertyHmolar,O2(g),temperature=T:h_H2O≔Chemicals:-PropertyHmolar,H2O(g),temperature=T:h_CO2≔Chemicals:-PropertyHmolar,CO2(g),temperature=T:
Enthalpy of the reactants
H_reactants≔1mol⋅ h_f_C4H10
−150.66kJ
Total enthalpy of the combustion products
H_products≔4 mol⋅ h_CO2+ 5 mol ⋅ h_H2O+ 24.44 mol ⋅ h_N2
H_products≔4Chemicals:−PropertyHmolar,CO2(g),temperature=Tmol+5Chemicals:−PropertyHmolar,H2O(g),temperature=Tmol+24.44Chemicals:−PropertyHmolar,N2(g),temperature=Tmol
Equating the enthalpy of the reactants and the enthalpy of the combustion products gives the adiabatic flame temperature
fsolveH_reactants=H_products,T=2000K
2379.85K
Application: Equilibrium Composition of the Combustion of Carbon Monoxide and Oxygen
One mole of CO and 0.5 moles of O2 are burned at 3000 K
CO (g) + 0.5 O2 (g) → CO2 (g)
The combustion products undergo dissociation and contain CO2, CO, O and O2. Here, we will calculate the equilibrium composition of the combustion products
Physical Properties
Enthalpies as a function of temperature
h_CO≔Chemicals:-PropertyHmolar,CO(g),temperature=T:h_C≔Chemicals:-PropertyHmolar,C(gr),temperature=T:h_O2≔Chemicals:-PropertyHmolar,O2(g),temperature=T:h_O≔Chemicals:-PropertyHmolar,O(g),temperature=T:h_CO2≔Chemicals:-PropertyHmolar,CO2(g),temperature=T:
Entropy as a function of temperature
s_CO≔Chemicals:-PropertySmolar,CO(g),temperature=T: s_C≔Chemicals:-PropertySmolar,C(gr),temperature=T:s_O2≔Chemicals:-PropertySmolar,O2(g),temperature=T:s_O≔Chemicals:-PropertySmolar,O(g),temperature=T:s_CO2≔Chemicals:-PropertySmolar,CO2(g),temperature=T:
Gibbs Free Energy as a function of temperature
G_CO ≔ T→h_CO − h_C+0.5⋅ h_O2−T⋅s_CO − s_C+0.5⋅ s_O2:G_CO2 ≔ T→h_CO2 − h_C+h_O2−T⋅s_CO2 − s_C+s_O2:G_O2 ≔ T→0:G_O ≔ T→h_O − 0.5⋅h_O2−T⋅s_O − 0.5 ⋅s_O2:
Universal gas constant
R≔8.314 J mol−1 K−1:
Constraints
Balancing the reactants and products gives
CO + 0.5 O2 = n1 CO2 + n2 CO + n3 O + n4 O2
This results in the following constraint on the oxygen atoms...
con1≔2n1+n2+n3+2n4=2 mol:
...and this constraint on the carbon atoms
con2≔n1+n2=1 mol:
Total number of moles in products
nt≔n1+n2+n3+n4:
Equilibrium Composition
For a given temperature, minimizing the Gibbs Free Energy of the combustion products will give the equilibrium molar composition
gibbs≔n1G_CO2T+RTlnn1nt+n2G_COT+RTlnn2nt+n3G_OT+RTlnn3nt+n4G_O2T+RTlnn4nt:
res≔Optimization:-Minimizeevalgibbs,T=3000K,con1,con2,n1≥0.0001 mol,n2≥0.0001 mol,n3≥0.0001 mol,n4≥0.0001 mol
−4.16167796100690844105J,n1=0.545813996336248mol,n2=0.454186003663752mol,n3=0.0565244627353324mol,n4=0.198830770464210mol
Updated CoolProp Library
Maple 2018 updates the CoolProp library to version 6.1. This includes new fluids and updated routines used to calculate fluid properties.
New fluids include Dichloroethane, DiethylEther, EthyleneOxide, HydrogenChloride, Novec 649TM and several others.
Propertyenthalpy,R245ca,temperature=298K,pressure=1atm
233.86kJkg
PropertyPcrit,DiethylEther, useunits
3.649MPa
Updated ScientificConstants Package
The non-derived physical constants in the ScientificConstants package now reflect the most recent values published by CODATA.
withScientificConstants
AddConstant,AddElement,AddProperty,Constant,Element,GetConstant,GetConstants,GetElement,GetElements,GetError,GetIsotopes,GetProperties,GetProperty,GetUnit,GetValue,HasConstant,HasElement,HasProperty,ModifyConstant,ModifyElement
GetConstantG
Newtonian_constant_of_gravitation,symbol=G,value=6.6740810−11,uncertainty=3.110−15,units=m3kgs2
Applications
Theoretical Rocket Performance
Rich and Lean Octane Combustion
Equilibrium Composition and Flame Temperature of the Combustion of Carbon Monoxide
Deflagration Pressure of the Combustion of Hydrogen in Air at Constant Volume
Spontaneity of the Reaction of N2 and O2 to form NO
Gibbs Energy of Formation of Ethanol
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