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 Thermophysical and Thermodynamic Data

Introduction

The ThermophysicalData package contains tools that give the thermophysical properties of pure fluids and fluid mixtures, and the thermodynamic properties of various chemical species.

 > $\mathrm{with}\left(\mathrm{ThermophysicalData}\right)$
 $\left[{\mathrm{Chemicals}}{,}{\mathrm{CoolProp}}{,}{\mathrm{PHTChart}}{,}{\mathrm{Property}}{,}{\mathrm{PsychrometricChart}}{,}{\mathrm{TemperatureEntropyChart}}\right]$ (1)

Pure Fluid and Mixture Properties

The temperature of water using pressure and enthalpy as states.

 >
 ${392.1848707}{}⟦{K}⟧$ (2)

You can also calculate the properties of fluid mixtures. This, for example, is the density of a molar mixture of methane, ethane, n-butane and pentane, using temperature and pressure as states.

 >
 ${1.421700878}{}⟦\frac{{\mathrm{kg}}}{{{m}}^{{3}}}⟧$ (3)

Chemical Species

The ThermophysicalData:-Chemicals subpackage contains functions that give the enthalpy, entropy, and specific heat capacity of over 2000 species at standard pressure. You can also extract the heat of formation and molecular weight.

The heat of formation and molecular weight of CO2

 > $\mathrm{Chemicals}:-\mathrm{Property}\left("HeatOfFormation","CO2\left(g\right)",\mathrm{useunits}\right);\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}$$\mathrm{Chemicals}:-\mathrm{Property}\left("MolarMass","CO2\left(g\right)",\mathrm{useunits}\right)$
 ${-}{393510.000}{}⟦\frac{{J}}{{\mathrm{mol}}}⟧$
 ${44.0095000}{}⟦\frac{{g}}{{\mathrm{mol}}}⟧$ (4)

Enthalpy and entropy of CO2 at 300 K and 1 bar

 >
 ${-}{3.934412212}{}{{10}}^{{5}}{}⟦\frac{{J}}{{\mathrm{mol}}}⟧$
 ${214.0173732}{}⟦\frac{{J}}{{\mathrm{mol}}{}{K}}⟧$ (5)

An empirical correlation for the enthalpy of CO2 as function of temperature

 > $\mathrm{Chemicals}:-\mathrm{Property}\left("Hmolar","CO2\left(g\right)","temperature"=\mathrm{T},\mathrm{explicit}\right);$
 ${8.314510}{}{T}{}\left(\left\{\begin{array}{cc}{-}\frac{{49436.50540}}{{{T}}^{{2}}}{-}\frac{{626.4116010}{}{\mathrm{ln}}{}\left({T}\right)}{{T}}{+}{5.301725240}{+}{0.001251906908}{}{T}{-}{7.091029093}{}{{10}}^{{-8}}{}{{T}}^{{2}}{-}{1.922497195}{}{{10}}^{{-10}}{}{{T}}^{{3}}{+}{5.699355602}{}{{10}}^{{-14}}{}{{T}}^{{4}}{-}\frac{{45281.98460}}{{T}}& {200.000}{<}{T}{\le }{1000.000}\\ {-}\frac{{117696.2419}}{{{T}}^{{2}}}{-}\frac{{1788.791477}{}{\mathrm{ln}}{}\left({T}\right)}{{T}}{+}{8.291523190}{-}{0.00004611578390}{}{T}{+}{1.621225627}{}{{10}}^{{-9}}{}{{T}}^{{2}}{-}{4.727633280}{}{{10}}^{{-13}}{}{{T}}^{{3}}{+}{1.266007318}{}{{10}}^{{-16}}{}{{T}}^{{4}}{-}\frac{{39083.50590}}{{T}}& {1000.000}{<}{T}{\le }{6000.000}\\ \frac{{1.544423287}{}{{10}}^{{9}}}{{{T}}^{{2}}}{+}\frac{{1.016847056}{}{{10}}^{{6}}{}{\mathrm{ln}}{}\left({T}\right)}{{T}}{-}{256.1405230}{+}{0.01684700540}{}{T}{-}{7.270614457}{}{{10}}^{{-7}}{}{{T}}^{{2}}{+}{1.747855210}{}{{10}}^{{-11}}{}{{T}}^{{3}}{-}{1.768470300}{}{{10}}^{{-16}}{}{{T}}^{{4}}{-}\frac{{8.043214510}{}{{10}}^{{6}}}{{T}}& {6000.000}{<}{T}{\le }{20000.000}\end{array}\right\\right)$ (6)

Thermodynamic Visualizations

The ThermophysicalData package also generates several visualizations for each of the pure fluids. These are standard Maple plot objects, so you can place lines and other visual elements on them to indicate the path of a thermodynamic cycle.

 > $\mathrm{PHTChart}\left(\mathrm{R410a}\right)$
 > $\mathrm{TemperatureEntropyChart}\left(\mathrm{water}\right)$



Humid Air Properties and Psychrometric Charts

You can calculate the properties of humid air. Here we calculate the specific enthalpy of humid air at a user-defined dry-bulb temperature, pressure and relative humidity.

 > $\mathrm{Property}\left(\mathrm{Hha},\mathrm{HumidAir},\mathrm{Tdb}=293⟦\mathrm{K}⟧,\mathrm{pressure}=101325⟦\mathrm{Pa}⟧,\mathrm{R}=0.45\right)$
 ${36.20964300}{}⟦\frac{{\mathrm{kJ}}}{{\mathrm{kg}}}⟧$ (7)

You can generate a psychrometric chart, and use it to visualize heating/cooling by overlaying plot objects on it. For example, see the Human Comfort Zone application.

 > $\mathrm{PsychrometricChart}\left(\mathrm{pressure}=101325⟦\mathrm{Pa}⟧\right)$

Computing with Thermophysical Data

The ThermophysicalData package provides thermodynamic and transport properties in a computable format. This means you can use fluid properties with all of Maple math tools, including the optimizers, numerical integrators and more.

Isothermal Compression

Here, for example, we compute the work done (in J kg-1) in the isothermal compression of propane from a specific volume of 1 m3 kg-1 to 0.5 m3 kg-1. This involves the use of numerical integrators

 >
 >
 ${-45330.42277}$ (1.1)

Here we calculate the flame temperature of butane. This involves the use of numerical solvers.

Liquid butane is burnt with 100% stoichiometric 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)

Heat of formation of butane

 > $\mathrm{h_f_C4H10}≔\mathrm{Chemicals}:-\mathrm{Property}\left("HeatOfFormation","C4H10\left(l\right),n-buta",\mathrm{useunits}\right)$
 ${-}{150.6640000}{}⟦\frac{{\mathrm{kJ}}}{{\mathrm{mol}}}⟧$ (2.1)

Enthalpies of the combustion products at a temperature T

 > $\mathrm{h_N2}≔\mathrm{Chemicals}:-\mathrm{Property}\left("Hmolar","N2\left(g\right)","temperature"=\mathrm{T}\right):$$\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\mathrm{h_O2}≔\mathrm{Chemicals}:-\mathrm{Property}\left("Hmolar","O2\left(g\right)","temperature"=\mathrm{T}\right):\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}$$\mathrm{h_H2O}≔\mathrm{Chemicals}:-\mathrm{Property}\left("Hmolar","H2O\left(g\right)","temperature"=\mathrm{T}\right):\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}$$\mathrm{h_CO2}≔\mathrm{Chemicals}:-\mathrm{Property}\left("Hmolar","CO2\left(g\right)","temperature"=\mathrm{T}\right):$

Enthalpy of the reactants

 >
 ${-}{150.6640000}{}⟦{\mathrm{kJ}}⟧$ (2.2)

Total enthalpy of the combustion products

 >
 ${\mathrm{H_products}}{≔}{4}{}{\mathrm{Chemicals}}{:-}{\mathrm{Property}}{}\left({"Hmolar"}{,}{"CO2\left(g\right)"}{,}{"temperature"}{=}{T}\right){}⟦{\mathrm{mol}}⟧{+}{5}{}{\mathrm{Chemicals}}{:-}{\mathrm{Property}}{}\left({"Hmolar"}{,}{"H2O\left(g\right)"}{,}{"temperature"}{=}{T}\right){}⟦{\mathrm{mol}}⟧{+}{24.44}{}{\mathrm{Chemicals}}{:-}{\mathrm{Property}}{}\left({"Hmolar"}{,}{"N2\left(g\right)"}{,}{"temperature"}{=}{T}\right){}⟦{\mathrm{mol}}⟧$ (2.3)

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

 > $\mathrm{fsolve}\left(\mathrm{H_reactants}=\mathrm{H_products},\mathrm{T}=2000⟦\mathrm{K}⟧\right)$
 ${2379.853026}{}⟦{K}⟧$ (2.4)
 >

 Thermophysical Properties Calculator The Thermophysical Properties Calculator provides a graphical interface for extracting fluid properties and generating charts.

 Applications Thermal Engineering Maximize the Efficiency of a Rankine Cycle Condition Air into the Human Comfort Zone Flow of R717 through an Expansion Valve Organic Rankine Cycle Mixing Humid Air Heat Transfer Coefficient across a Flat Plate Energy Required to Vaporize Ethanol Particle Falling through Air Saturation Temperature of Fluids