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So I have

Emin[T_, d_] := If[T == 0, 0, 1/(-1 + E^(1/T)) - d/(-1 + E^(d/T))];

which I can solve wonderfully for

Solve[Emin[T, 10] == 0.5, T, Reals]

{{T -> 0.910427}}

Now as you see Emin[T_, d_] is also dependent on d which I set to d=10 in the second line.

All I'd like is to now Plot this solve for different d.

I've got so far this:

Tlist = Table[Solve[Emin[T, d] == 0.5, T, Reals] // Values // Flatten // N, {d, 5, 10}]

{{0.936864}, {0.919994}, {0.913886}, {0.911604}, {0.910747}, {0.910427}}

But as you see I cannot plot this because d is missing in those entries.

So can anyone either help me add the correct d value to the entries or maybe help me plot this even simpler? Thanks in advance !

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Reformatting a little:

Emin[T_, d_] := If[T == 0, 0, 1/(-1 + E^(1/T)) - d/(-1 + E^(d/T))]; 
Tlist = Table[{d, First[Solve[Emin[T, d] == 0.5, T, Reals] 
              // Values // Flatten // N]}, {d, 5, 10}] // Quiet

ListPlot[Tlist]

enter image description here

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With the additional information d01,2,3...10 try

dT = Table[{d, T /. NSolve[Emin[T, d] == 0.5, T, Reals][[1]]}, {d, 1,10}]
(*{{1, T /. {}[[1]]}, {2, T /. {}[[1]]}, {3, 1.19888}, {4,0.988141},
{5, 0.936864}, {6, 0.919994}, {7, 0.913886}, {8,0.911604}, {9, 0.910747}, {10, 0.910427}}*)

Show[ContourPlot[Emin[T, d] == 0.5, {d, 0, 10}, {T, .5, 2},FrameLabel -> {T, d}], Graphics[Point[dT[[3 ;;]]]]]

enter image description here

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  • $\begingroup$ That is a step in the right direction but I'd rather have d on the x-axis and T on the y axis. Also d can have only integer numbers. Sorry should have mentioned that i.e. d = 1,2,3,...,10. $\endgroup$ – CatoMaths Feb 5 at 20:19
  • $\begingroup$ That being said does it have to be a ContourPlot ? I'd rather have only a x-y axis instead of a box. Sorry if this is to much $\endgroup$ – CatoMaths Feb 5 at 20:25

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