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5-17 - "'r —_1=u"-I Problem 5.17 The enthalpy and...

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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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