ThermodynamicData
Interpolation
Derivative
Quantity
ListLinePlot
UnitConvert
UnitSimplify

Physics
Chemistry
Data Science

Compute Thermodynamic Values from Interpolated Data

Calculate the heat capacity of carbon dioxide from interpolated volume data

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Use

ThermodynamicData

to get the volume data for

at constant temperature:

In[1]:=

refTemperature=Quantity[40,"DegreesCelcius"];With[{p=

Table[

,{x,4,6,0.01}]Pa

},constantT=Transpose[{p,ThermodynamicData["CarbonDioxide","SpecificVolume",{"Pressure"p,"Temperature"refTemperature}]}]];

Get the data at constant pressure:

In[2]:=

refPressure=

;With[{t=Quantity[Table[x,{x,30,50,0.1}],"DegreesCelcius"]},constantP=Transpose[{t,ThermodynamicData["CarbonDioxide","SpecificVolume",{"Temperature"t,"Pressure"refPressure}]}]];

Interpolate over the data to get

∂V

∂P

and

∂V

∂T

In[3]:=

dVdP[x_Quantity]:=Derivative[1][Interpolation[constantT]][x];dVdT[x_Quantity]:=Derivative[1][Interpolation[constantP]][x];

Plot the estimated derivatives:

In[4]:=

ColumnListLinePlotTable[With[{tt=Quantity[10^p,"Pascals"]},{tt,dVdP[tt]}],{p,4,6,0.01}],

,ListLinePlotTable[{Quantity[t,"DegreesCelcius"],dVdT[Quantity[t,"DegreesCelcius"]]},{t,30,50,0.1}],



Out[4]=

Use the relation



-T

δV

δT



δV

δP

and the interpolated data to compute the isobaric heat capacity from the isochoric heat capacity:

In[5]:=

Cv=ThermodynamicData["CarbonDioxide","IsochoricHeatCapacity",{"Temperature"refTemperature,"Pressure"refPressure}];Cv-UnitConvert[refTemperature,"Kelvins"]*UnitSimplify[((dVdT[refTemperature]^2)/dVdP[refPressure])]

Out[5]=

865.063

J/(kgK)

Compare the computed result with available data:

In[6]:=

ThermodynamicData["CarbonDioxide","IsobaricHeatCapacity",{"Temperature"refTemperature,"Pressure"refPressure}]

Out[6]=

865.058

J/(kgK)

Related Symbols

ThermodynamicData
Interpolation
Derivative
Quantity
ListLinePlot
UnitConvert
UnitSimplify

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Contributed by: Wolfram Staff