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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

(2.1)

Heat of formation and molar mass of gaseous CO2

Chemicals:-PropertyHeatOfFormation,CO2(g),useunits;Chemicals:-PropertyMolarMass,CO2(g),useunits;

3.93510000105Jmol

44.0095000gmol

(2.2)

Enthalpy and entropy of gaseous CO2 at 300 K

Chemicals:-PropertyHmolar,CO2(g),temperature=300 K;Chemicals:-PropertySmolar,CO2(g),temperature=300 K;

3.934412212105Jmol

214.0173732JmolK

(2.3)

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_C4H10Chemicals:-PropertyHeatOfFormation,C4H10(l),n-buta,useunits

150.6640000kJmol

(2.1.1)

Enthalpies of the combustion products at a temperature T

h_N2Chemicals:-PropertyHmolar,N2(g),temperature=T:h_O2Chemicals:-PropertyHmolar,O2(g),temperature=T:h_H2OChemicals:-PropertyHmolar,H2O(g),temperature=T:h_CO2Chemicals:-PropertyHmolar,CO2(g),temperature=T:

 

Enthalpy of the reactants

H_reactants1mol h_f_C4H10

150.6640000kJ

(2.1.2)

Total enthalpy of the combustion products

H_products4 mol h_CO2+ 5 mol  h_H2O+ 24.44 mol  h_N2

H_products4Chemicals:−PropertyHmolar,CO2(g),temperature=Tmol+5Chemicals:−PropertyHmolar,H2O(g),temperature=Tmol+24.44Chemicals:−PropertyHmolar,N2(g),temperature=Tmol

(2.1.3)

 

Equating the enthalpy of the reactants and the enthalpy of the combustion products gives the adiabatic flame temperature

fsolveH_reactants=H_products,T=2000K

2379.853026K

(2.1.4)

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_COChemicals:-PropertyHmolar,CO(g),temperature=T:h_CChemicals:-PropertyHmolar,C(gr),temperature=T:h_O2Chemicals:-PropertyHmolar,O2(g),temperature=T:h_OChemicals:-PropertyHmolar,O(g),temperature=T:h_CO2Chemicals:-PropertyHmolar,CO2(g),temperature=T:

 

Entropy as a function of temperature

s_COChemicals:-PropertySmolar,CO(g),temperature=T: s_CChemicals:-PropertySmolar,C(gr),temperature=T:s_O2Chemicals:-PropertySmolar,O2(g),temperature=T:s_OChemicals:-PropertySmolar,O(g),temperature=T:s_CO2Chemicals:-PropertySmolar,CO2(g),temperature=T:

 

Gibbs Free Energy as a function of temperature

G_CO  Th_CO  h_C+0.5 h_O2Ts_CO  s_C+0.5 s_O2:G_CO2  Th_CO2  h_C+h_O2Ts_CO2s_C+s_O2:G_O2  T0:G_O  Th_O  0.5h_O2Ts_O  0.5 s_O2:

 

Universal gas constant

R8.314 J mol1 K1:

 

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...

con12n1+n2+n3+2n4=2 mol:

 

...and this constraint on the carbon atoms

con2n1+n2=1 mol:

 

Total number of moles in products

ntn1+n2+n3+n4:

 

Equilibrium Composition

For a given temperature, minimizing the Gibbs Free Energy of the combustion products will give the equilibrium molar composition

gibbsn1G_CO2T+RTlnn1nt+n2G_COT+RTlnn2nt+n3G_OT+RTlnn3nt+n4G_O2T+RTlnn4nt:

resOptimization:-Minimizeevalgibbs,T=3000K,con1,con2,n10.0001 mol,n20.0001 mol,n30.0001 mol,n40.0001 mol

4.16167796100690844105J,n1=0.545813996336248mol,n2=0.454186003663752mol,n3=0.0565244627353324mol,n4=0.198830770464210mol

(2.2.3.1)

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

233.8629511kJkg

(3.1)

PropertyPcrit,DiethylEther, useunits

3.649016897MPa

(3.2)

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

(4.1)

GetConstantG

Newtonian_constant_of_gravitation,symbol=G,value=6.6740810−11,uncertainty=3.110−15,units=m3kgs2

(4.2)

 

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