**Unformatted text preview: **"'__'r'__ _ ____ —__'_1=u' ' " _ -I.-' Problem 5.17. The enthalpy and Gibbs free energy, as deﬁned in this section, give
special treatment to mechanical (compression-expansion) work, _..p ("11". Analogous
quantities can be deﬁned for other kinds of work, for instance, magnetic workf
Consider the situation shown in Figure 5.7, where a long solenoid {N turns, total
length L) surrounds a magnetic specimen [perhaps a paramaﬂetic solid}. If the
magnetic ﬁeld inside the specimen is E and its total magnetic moment is lid, then
we deﬁne an amdlliary ﬁeld 1"? [often called simply the magnetic ﬁeld] by the relation where an is the “permeability of free space," as :s Iii—ir Ng’Az. Assuming cylindrical
symmetry, all vectors must point either left or right, so we can drop the " symbols
and agree that rightward is positive, leftward negative. From Ampere’s law, one
can also show that when the current in the wire is I, the 'H ﬁeld inside the solenoid is NHL, whether or not the specimen is present. (a) Imagine making an inﬁnitesimal change in the current in the wire, resulting
in inﬁnitesimal changes in B, M, and H. Use Fbraday‘s law to show that
the work required {from the power supply} to accomplish this change is
Wmtﬂl = V715 dB. [Neglect the resistance of the wire.) (b) Rewrite the result of part (a) in terms of ”H. and M, then subtract oﬁ' the work that would be required even if the specimen were not present. If
we deﬁne 'W‘,‘ the work done on the s;t,tsteirn,T to be what‘s left, show that W=nngM. (c) 1"What is the thermodynamic identity for this system? (Include magnetic
work but not mechanical work or particle ﬂow.) (d) How would you deﬁne analogues of the enthalpy and IGibbs free energy for
a magnetic system? [The Helmholts free energy is deﬁned in the same way
as for a mechanical system.) Derive the thermodynamic identities for each
of these quantities, and discuss their interpretations. Figure 5.7. A long solenoid, surrounding a magnetic specimen, connected
to a power supply that can change the current, performing magnetic work. =|=This problem requires some familiarity with the theory of magnetism in matter. See,
for instance, David J. Griﬁiths, Introduction to Electrodynamics, third edition {Prentice- Hall, Englewood Cliffs, NJ, 1999}, Chapter 6.
lThis is not the only possible deﬁnition of the “system.“ Different deﬁnitions are
suitable for different physical situations, unfortunately leading to much confusion in ter- minology. For a more complete discussion of the thermodynamics of magnetism see Mandi
{1933}, Carrington {1994], andfor Pippard {1957]. '3 ...

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