function P2_13
clear, clc, format short g, format compact
xguess = 2000. ; 
disp('Variable values at the initial estimate');
disp([' Unknown value ' num2str(xguess) '   Function Value ' num2str(NLEfun(xguess))]); 
xsolv=fzero(@NLEfun,xguess); 
disp(' Variable values at the solution');
disp([' Unknown value ' num2str(xsolv) '   Function Value ' num2str(NLEfun(xsolv))]); 
%- - - - - - - - - - - - - - - - - - - - - -
function fT = NLEfun(T); 
y = .75; 
x = .5; 
z = 1 - y - .02; 
if (x < 1) 
    CH4 = y * (1 - x);
else
    CH4 = 0;
end 
if (x < 1) 
    C2H6 = z * (1 - x);
else
    C2H6 = 0;
end 
if (x < 1) 
    CO2 = (y + 2 * z) * x;
else
    CO2 = y + 2 * z;
end 
if (x < 1) 
    H2O = (2 * y + 3 * z) * x;
else
    H2O = 2 * y + 3 * z;
end 
N2 = .02 + 3.76 * (2 * y + 7 * z / 2) * x; 
alp = 3.381 * CH4 + 2.247 * C2H6 + 6.214 * CO2 + 7.256 * H2O + 6.524 * N2; 
bet = 18.044 * CH4 + 38.201 * C2H6 + 10.396 * CO2 + 2.298 * H2O + 1.25 * N2; 
gam = -4.3 * CH4 - (11.049 * C2H6) - (3.545 * CO2) + .283 * H2O - (.001 * N2); 
H0 = alp * 298 + bet * .001 * 298 * 298 / 2 + gam * 10 ^ -6 * 298 ^ 3 / 3; 
Hf = alp * T + bet * .001 * T ^ 2 / 2 + gam * .000001 * T ^ 3 / 3; 
fT = 212798 * y * x + 372820 * z * x + H0 - Hf;