Express the volume expansivity and the isothermal compressibility as functions of density rho and its partial derivatives. For water at 50°C and 1 bar, κ = 44.18 × 10 −6 bar −1 . To what pressure must water be compressed at 50°C to change its density by 1%? Assume that κ is independent of P.

Certain bacteria (such as aquaspirillum magnetotacticum) tend to swim toward the earth’s geographic north pole because they contain tiny particles, called magnetosomes, that are sensitive to a magnetic field. if a transmission line carrying 100 a is laid underwater, at what range of distances would the magnetic field from this line be great enough to interfere with the migration of these bacteria? (assume that a field less than 5% of the earth’s field would have little effect on the bacteria. take the earth’s field to be 5.0 * 10-5 t, and ignore the effects of the seawater.)