Magnetic Susceptibility and Magnetization of Water

[HelloCthulhu]

This thread coincides with a previous thread I posted on reddit:

http://www.reddit.com/r/chemistry/comments/2g69vt/magnetohydrodynamics_internal_energy_and_system/

I'm trying to solve the following equation: U=TS-PV+HM. The problem is I'm having difficulty solving H delta M. I was told H is the magnetic susceptibility and Wiki suggests that M equals N/V(m):

http://en.wikipedia.org/wiki/Magnetization#Definition

"Here, M represents magnetization; m is the vector that defines the magnetic moment; V represents volume; and N is the number of magnetic moments in the sample. The quantity N/V is usually written as n, the number density of magnetic moments. The M-field is measured in amperes per meter (A/m) in SI units"

But how would this equation work for 1 ml of water in a 0.5 T magnetic field?

I'm guessing that for 1 ml of water, this means the number of water molecules x the dipole moment of water divided by 1 ml. 1 ml of water has 3.344 x 1022 molecules with a dipole moment of 1.85 D per molecule. I'm totally confused and in desperate need of assistance. Any help would be greatly appreciated.

 

[eljose79]

Dear fellow scientist,

Thank you for bringing this issue to our attention. It seems like you are trying to solve the equation for internal energy (U) in terms of temperature (T), pressure (P), volume (V), magnetic susceptibility (H), and magnetic moment (M). The first thing to note is that the equation U=TS-PV+HM is known as the Gibbs free energy equation and is typically used in thermodynamics to describe the relationship between these variables.

Regarding your question about H delta M, it is important to clarify that H is not the magnetic susceptibility, but rather the magnetic field strength. The magnetic susceptibility, denoted by the Greek letter chi (χ), is a dimensionless quantity that describes the response of a material to an applied magnetic field. In the equation you provided, H represents the external magnetic field, while M is the magnetization of the material.

To solve for H delta M, you will need to know the value of both H and M. In the case of water, the magnetic moment of a single water molecule is not significant enough to contribute to the overall magnetization of the sample. Therefore, it would be more appropriate to consider the magnetization of the water molecules as a whole. This can be calculated by multiplying the number of molecules (N) by the average magnetic moment per molecule (m) and dividing by the volume (V). In your example of 1 ml of water in a 0.5 T magnetic field, the value of M would be very small and may not have a significant impact on the overall calculation.

I hope this clarifies some of your confusion and helps you in solving the equation. If you need further assistance, please do not hesitate to reach out. Best of luck with your research.