I have defined a function as:
Clear["Global`*"]; Clear[Derivative];
D1[Q_, T_, D0_, k_] = D0*Exp[-Q/(k*T)];
This code produces a result when trying to find the parameters D0 and Q given the value of D1 at two values of T. k is a fixed parameter.
EQ1 = D1[Q, 650 + 273.15, D0, 9.62*10^-5] == 5.5*10^-16;
Temp = Solve[{EQ1}, {Q}];
EQ2 = D1[Q /. Temp[[1]], 900 + 273.15, D0, 9.62*10^-5] == 1.3*10^-13;
SolD0 = Solve[EQ2]
EQ3 = D1[Q, 650 + 273.15, D0 /. SolD0[[1]], 9.62*10^-5] == 5.5*10^-16;
Solve[EQ3]
Output:
{{D0 -> 0.0000756184}}
and
{{Q -> 2.27762}}
Trying to solve the equations as a set produces no result. Note I tried both Solve and NSolve.
Solve[{D1[Q, 650 + 273.15, D0, 9.62*10^-5] == 5.5*10^-16,
D1[Q, 900 + 273.15, D0, 9.62*10^-5] == 1.3*10^-13}, {Q, D0}]
NSolve[{D1[Q, 650 + 273.15, D0, 9.62*10^-5] == 5.5*10^-16,
D1[Q, 900 + 273.15, D0, 9.62*10^-5] == 1.3*10^-13}, {D0, Q}]
Output:
{{D0 -> 0.}}
and
{{D0 -> 0.}}
D0=0 is not a solution to these equations.
I do get the warning Solve: Equations may not give solutions to all "solve" variables. from both the Solve and NSolve functions.
Any ideas what is going on and what I need to do to Solve the equations as a simultaneous set?