Question

has a magnetic field 거 which induces magnetization of the material M. I he tree is Assume constant temperature so (a) Derive a Maxwell relationship between the magnetic field and the volume. aoes hot ma (b) Make a Legendra transformation from G(P, M) to G'(P, H) and express dG. dar (c) Use G' to derive an expression for d P dH at equilibrium (dG-0). What does this mean physically?

Answer 1

d G = v d P + Hd M ---- (1) (a) we an derive Maxwell's equation from using the fact that the differentials of the thermodynamic potentials are exact Now, we know for any three variable x, y, z we have a relation of the form rightarrow d z = M (x, y) d x + N (x, y) d y -- (2) Therefore The differential d z is exact if (partial differential M/ partial differential y)_x = (partial differential N/ partial differential x)_y --- (3) Hence, comparing the variables of equation (1) with equation (2) we can see rightarrow z = G, M = V, x = P, N = M: y = M: Now, since d G is exact we can write in the same spirit as equation (3) rightarrow (partial differential v/ partial differential M)_p = (partial differential M/ partial differential p)_M --- (4)