Thermodynamic curvature of the multicomponent ideal gas

We work out the thermodynamic curvature resulting from a Riemannian geometric approach to thermodynamics for the general multicomponent ideal gas. This Riemannian geometry is based on including fluctuation theory in thermodynamics. We find that the Riemannian curvature scalar for this system is small, on the order of the average volume per molecule, no matter how many components. This result fits in well with expectations developed earlier that the thermodynamic curvature gives a measure of the volume where classical thermodynamic fluctuation theory fails.