Compute Thermodynamic Values from Interpolated Data 

Get the volume data for at constant pressure and constant temperature from ThermodynamicData.

show complete Wolfram Language inputhide input

In[1]:=

X refTemperature = Quantity[40, "DegreesCelcius"]; refPressure = Quantity[10^5, "Pascals"]; With[{p = Quantity[Table[10^x, {x, 4, 6, 0.01}], "Pascals"]}, constantT = Transpose[{p, ThermodynamicData["CarbonDioxide", "SpecificVolume", {"Pressure" -> p, "Temperature" -> refTemperature}]}]]; 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 and get and .

In[2]:=

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

Plot the estimated derivatives.

show complete Wolfram Language inputhide input

In[3]:=

X Column[{ ListLinePlot[ Table[With[{tt = Quantity[10^p, "Pascals"]}, {tt, dVdP[tt]}], {p, 4, 6, 0.01}], Frame -> True, FrameLabel -> Automatic, PlotLabel -> "\!\(\*SubscriptBox[\((\*FractionBox[\(\[PartialD]V\), \(\ \[PartialD]p\)])\), \(T\)]\)", ImageSize -> Medium], ListLinePlot[ Table[{Quantity[t, "DegreesCelcius"], dVdT[Quantity[t, "DegreesCelcius"]]}, {t, 30, 50, 0.1}] , Frame -> True, FrameLabel -> Automatic, PlotLabel -> "(\!\(\*FractionBox[\(\[PartialD]V\), \ \(\[PartialD]T\)]\)\!\(\*SubscriptBox[\()\), \(p\)]\)", ImageSize -> Medium]}]

Out[3]=

Use the interpolated data to compute the isobaric heat capacity from the isochoric heat capacity.

In[4]:=

X Cv = ThermodynamicData["CarbonDioxide", "IsochoricHeatCapacity", {"Temperature" -> refTemperature, "Pressure" -> refPressure}];

In[5]:=

X Cv - UnitConvert[refTemperature, "Kelvins"]* UnitSimplify[((dVdT[refTemperature]^2)/ dVdP[refPressure])*(Quantity[1, "Kilograms"]/ Quantity[1, "Moles"])]

Out[5]=

Compare the computed result with available data.

In[6]:=

X ThermodynamicData["CarbonDioxide", "IsobaricHeatCapacity", \ {"Temperature" -> refTemperature, "Pressure" -> refPressure}]

Out[6]=