A1 = 817.08;
A2 = 1051.38;
A3 = 1267.56;
A4 = 1183.44;
B1 = 4.402229;
B2 = 4.517190;
B3 = 4.617679;
B4 = 4.474013;
x1 = .05;
x2 = .10;
x3 = .40;
x4 = .45;
P = 5;
None of those lines define T
iterateBubble = @(T) ((x1*(10^(-(A1/T) + B1)))/P) + ((x2*(10^(-(A2/T) + B2)))/P) + ((x3*(10^(-(A3/T) + B3)))/P) + ((x4*(10^(-(A4/T) + B4)))/P)
That line does not define a variable named T. Instead, it defines a variable named iterateBubble as a handle to an anonymous function. The anonymous function is passed in a single parameter, which for the purposes of the function body will be referred to as T only within the function body . At the time the anonymous function is executed, whatever value is passed in to the function handle will be used in place of references to T in executing the statement. The effect is similar to if you had written
iterateBubble = @iterateBubble_implementation
function result = iterateBubble_implementation(T)
result = ((x1*(10^(-(A1/T) + B1)))/P) + ((x2*(10^(-(A2/T) + B2)))/P) + ((x3*(10^(-(A3/T) + B3)))/P) + ((x4*(10^(-(A4/T) + B4)))/P);
end
in that in both cases, T is a dummy variable that stands in for the value passed in and does not get assigned to inside the calling workspace.
vpasolve(iterateBubble(T) == 1, T)
That tries to pass the variable T into iterateBubble, and tries to use variable T as the second parameter to vpasolve(), but no variable named T has been created.
You can repair this problem by adding this line above the call to vpasolve:
syms T
