Let's say I define a function giving the enthalpy of water:

f[t_]:=QuantityMagnitude@ThermodynamicData["Water","Enthalpy",{"Pressure"->Quantity[1,"Bars"], "Temperature"->Quantity[t,"DegreesCelsius"]}]

I'd like to use that to find out what temperature corresponds to a given enthalpy:


But this gives me no result. Is there a way to do it?


Restrict the argument of f to numeric values:

f[t_?NumericQ] := QuantityMagnitude @ ThermodynamicData[
    {"Pressure"->Quantity[1,"Bars"], "Temperature"->Quantity[t,"DegreesCelsius"]}

Then, you can just use FindRoot:

FindRoot[f[t] == 300000, {t, 50}]

{t -> 71.6414}

  • $\begingroup$ Interesting. I had tried that with NSolve but it didn't work, so I assumed it wouldn't work with FindRoot either. $\endgroup$ – Whelp May 16 at 15:23

How about generating an interpolation over the expected range and use FindRoot like so?

f = Interpolation@
       "Enthalpy", {"Pressure" -> Quantity[1, "Bars"], 
        "Temperature" -> Quantity[t, "DegreesCelsius"]}]}, {t, 1, 
FindRoot[f[t] - 300000, {t, 50}]
(* {t -> 71.6414} *)

Also, if you are just interested in having temperature as a function of enthalpy, you could transpose the table and avoid FindRoot all together.

tofh = Interpolation@
       "Enthalpy", {"Pressure" -> Quantity[1, "Bars"], 
        "Temperature" -> Quantity[t, "DegreesCelsius"]}], t}, {t, 1, 
     99, 10}];
(* 71.6414 *)
  • $\begingroup$ That's a method I've been considering. I was worried it might be very slow. $\endgroup$ – Whelp May 16 at 14:45
  • $\begingroup$ The database call is the slowest part. Once the table is populated, the interpolations are very fast. $\endgroup$ – Tim Laska May 16 at 14:47
  • $\begingroup$ I'll accept and give it a try. Given that behind the hood it's just calling a database, I doubt it can be made much more efficient than that. $\endgroup$ – Whelp May 16 at 14:50
  • $\begingroup$ If you are only interested in the liquid phase region, you need very few points. If you are near the boiling point, you may need a lot of points to capture the transition. I got the same answer when I stepped by 10 degrees. $\endgroup$ – Tim Laska May 16 at 14:53

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