Derive the extension of the gibbs-duhem equation for a paramagnetic fluid.
(hint: g=u+pv-μ0hm-ts).
use the above result to calculate the chemical potential of said fluid assuming it
is ideal, as a gas and as a magnetic system.

Abeam has a square cross-section, a x a, where a is the linear dimension, and is subject to a pure bending moment, m. m is known with an uncertainty of 10% and a is known with an uncertainty of 5%. the strength of the material is known to an uncertainty of 12%. find the minimum design factor such that the beam is guaranteed not to fail.

Unpolarized light of intensity i_0=750w/m^2 is incident upon two polarizers. after passing through both polarizers the intensity is i_2=280w/m^2. (a) what is the intensity of the light after it passes through the first polarizer in w/m^2? (b) write an equation for the angle between the polarizers in terms of the initial (i_0) and final (i_2) intensities. (c) find the angle between the polarizers in degrees.

Calculate the first and second velocities of the car with four washers attached to the pulley, using the formulas v1 = 0.25 m / t1 , and v2 = 0.25 m / (t2 – t1) where t1 and t2 are the average times the car took to reach the 0.25 and the 0.50 meter marks. record these velocities, to two decimal places, in table e.