The Planck Thermodynamic Potential of Water

Obtain the entropy, internal energy and specific volume of water at various temperatures and pressures, using

:

In[1]:=

temperature=UnitConvert[Quantity[Table[x,{x,20.,400,10}],"DegreesCelsius"],"Kelvins"];pressure=Quantity[Table[10^x,{x,3,6,0.1}],"Pascals"];opt={"Temperature"temperature,"Pressure"pressure};s=ThermodynamicData["Water","Entropy",opt];u=ThermodynamicData["Water","InternalEnergy",opt];v=ThermodynamicData["Water","SpecificVolume",opt];

Use the relation

Ξ(T,P)=S(T,P)-PV(T,P)/T-U(T,P)/T

to generate discrete values and perform 3D interpolation for the Planck potential or Gibbs free entropy:

In[2]:=

fun=Interpolation[Flatten[Table[{{temperature〚j〛,pressure〚i〛},s〚i,j〛-pressure〚i〛*(v〚i,j〛/temperature〚j〛)-u〚i,j〛/temperature〚j〛},{i,Length[pressure]},{j,Length[temperature]}],1]];

Plot the interpolated function as a function of temperature and pressure:

In[3]:=

Plot3Dfun[Quantity[t,"DegreesCelsius"],Quantity[p,"Pascals"]]1000,{t,20,400},{p,1000,10^6},



Out[3]=

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The Planck Thermodynamic Potential of Water

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