For \(CaGeO_3\), \(Z_m=20+32+8*3=76\) density \(3.56\,gcm^{-3}\) and molar mass \(160.7162\,gmol^{-1}\)
\(v_{boom}=3.4354*\cfrac{3560}{76}=160.92\,ms^{-1}\)
\(T_{v\,p}=160.92^2*\cfrac{160.7162*10^{-3}}{2*8.3144}=250.28\,K\) or \(-22.87\,^oC\)
which is still way low even with the use of \(v_p\) instead of \(v_{rms}\). Clearly,
\(T_{v\,p}\) or \(T_{boom}\propto density^2\) and
\(Conductivity\,at\,T_{v\,p}\gt Conductivity\,at\,T_{boom}\) due to more fraction of particles attaining \(v_{boom}\) at \( T_{v\,p}\). Conductivity is maximum at \(v_p=v_{boom}\) when \(Temperature=T_{v\,p}\).
The simple \(y=x^2\) relation of \(T_{v\,p}\) and \(T_{boom}\) with density is surprising given all the write-ups in superconductivity.
