Solving equation returns a 0x1 sym

I have two equations which I am trying to set equal to each other and solve, but it keeps returning "empty sym 0X1", and I'm not sure why. Any help? Intent to set S1=S2 and solve for T2. It works to give me a numeric value for S1, but can't get a solution for S2. Code below:

N=1000;
T1=300;
V1=.002;
V2=1*10^-5;
h=6.626*10^-34;
kb=1.38*10^-23;
g=3;
Sigma=2;
Thetav=2256;
m=3*10^-26;
r=(1.21*10^-10)/2;
I=m*r^2;
S1=N*kb*(log(((4*pi*m*kb*T1)/(h^2))*((V1*exp(5/2))/N)) + log((8*pi^2*I*kb*T1)/(Sigma*h^2)) + (Thetav*T1)/(exp(Thetav/T1)-1) - log(1-exp(-Thetav/T1)) + log(g))
S2=S1;
syms T2;
S2==N*kb*(log(((4*pi*m*kb*T2)/(h^2))*((V2*exp(5/2))/N)) + log((8*pi^2*I*kb*T2)/(Sigma*h^2)) + (Thetav*T2)/(exp(Thetav/T2)-1) - log(1-exp(-Thetav/T2)) + log(g));
solve(S2,T2)

Answer 1

[Walter Roberson]

N=1000;
T1=300;
V1=.002;
V2=1*10^-5;
h=6.626*10^-34;
kb=1.38*10^-23;
g=3;
Sigma=2;
Thetav=2256;
m=3*10^-26;
r=(1.21*10^-10)/2;
I=m*r^2;
S1=N*kb*(log(((4*pi*m*kb*T1)/(h^2))*((V1*exp(5/2))/N)) + log((8*pi^2*I*kb*T1)/(Sigma*h^2)) + (Thetav*T1)/(exp(Thetav/T1)-1) - log(1-exp(-Thetav/T1)) + log(g))
syms T2;
S2=N*kb*(log(((4*pi*m*kb*T2)/(h^2))*((V2*exp(5/2))/N)) + log((8*pi^2*I*kb*T2)/(Sigma*h^2)) + (Thetav*T2)/(exp(Thetav/T2)-1) - log(1-exp(-Thetav/T2)) + log(g));
solve(S1==S2,T2)

[Gary North]

Thanks, that does work to get a solution; but it gives an answer of 0, which isn't right. I've heard that for iterative solve equations you need to give it a guess value?

[Walter Roberson]

vpasolve(S1-S2,[1 5000])

[Gary North]

This gives me a T of 300.5, which is also definitely not accurate. It is possible it is my equations but I've checked them several times so I feel pretty confident they are accurate.

[Walter Roberson]

T2 of 300.5 is accurate to within the precision expressed by 300.5 .

fplot(S1-S2,[300 305])

You can fplot S2 to see that it is a strictly increasing function over the positives. It starts lower than S1 and increases, so there is a single point of interception.