Equation for the magnetic susceptibility of water

The new precision magnetic susceptibility data of Philo and Fairbank make it possible for the first time to look for a parallel between water’s response to a magnetic field and water’s response to an electric field. These volume susceptibility (κ) data measured at saturated vapor pressure over the temperature interval from 20 to 60 °C are found to satisfy the relationship, −γ−1(∂ln(−κ)/∂T)P=Bχ+Cχ(γ −1). Here γ=−(∂lnρ/∂T)P is the volume expansion coefficient and Bχ and Cχ are independent of temperature. Assuming Bχ and Cχ are also independent of density, we can integrate the above relationship to find This expression for κ describes the same volume magnetic susceptibility data of water to within its experimental uncertainty of two parts in one million. A similar relationship for water’s refractive index was previously shown by H. Eisenberg to fit all of the precision refractive index data of water to within its experimental uncertainty of one part in one million. The constant Cχ=−(∂ln(−κ)/∂T)ρ reflects the unusual temperature dependence of the volume magnetic susceptibility of water. The given expression for κ can be further tested by measuring (∂ln(−κ)/δP)T for water to see if the prediction β−1[∂ln(−κ)/∂P]T=Bχ=1.0213±0.0007 is observed experimentally. Here β=(∂lnρ/∂P)T is the isothermal compressibiltiy. Verification of the expression for κ would establish for the first time a close parallel between the electric polarizability and magnetic susceptibility of water.