From: mica@world.std.com (mitchell swartz)
Subject: silver (and other) wires
Organization: The World Public Access UNIX, Brookline, MA
Date: Sat, 12 Dec 1992 20:55:17 GMT


    There has been, and continues to be, much talk on this forum
 regarding nichrome and silver conductivity. 
 Some of the calculations (actually or rhetorically) requested 
 have been trivial, but the 'debate' continues, and so this table
 and elementary exercise are provided.

  For example [sci.physics.fusion:4480;  Jed Rothwell; Subject:
 Silver the same everywhere in the world; Date: Wed, 9 Dec 1992] states:

=     "the heater is: Ni-Cr two-ply wire (0.1 mm diameter, 40 mm length).
=   Just find out whether it is possible for any silver wire to generate 
=   as much heat as it does."

  or [sci.physics.fusion:4515; Subject: What Jones said; 11 Dec 1992]:

=  "Technical type people know damn well that the only way 6 cm of one wire
=   can dissipate as much heat as 4 cm of another wire is if both
=   have approximately the same resistance. They also know that it would take
=   an impossibly thin silver wire to be as resistant as a 0.5 nichrome wire".

   Now that Prof. Droege has vaulted this forum into discussions of
 electrodynamics, an elementary reminder of practical electrostatics
 is in order.  Impossibly thin?  How thin --->


   The electrical resistance (lumped parameter) characterizing a
 rod-like material  is a function of the electrical resistivity,
 the physical length, and cross-sectional area (presumed circular,
 with total homogeneity of material properties therein) as in

     rho * L   =  Resistance [ohms]
    --------
        A
                
   So the resistivity [rho: ohms-cm] {micro-ohms-cm in the table below
 which has the various materials listed by nichrome type
 (including the constitutional elements composing the various types),
 a common variety, and of course silver.  Temperature coefficients
 of the electrical resistance, and the effective temperature of that
 Taylor series simplification are also listed.  


  The nickel-chromiums were discovered in 1905 by Marsh, from which
 the electrical heating industry became generated.  A high resistance
 to oxidation, diverse patents based upon slight additions to the mix,
 and a need for such materials have generated diverse alloys.

  Notwithstanding the above, the electrical conductivity of a few
 can be compared to silver.

         ELECTRICAL CONDUCTIVITY OF A FEW MATERIALS

 [based in part upon Chemical Rubber Tables, and  Engineering Materials
         Handbook (Mantell) and Rare Metals Handbook (Hampel) ]

---------------------------------------------------------------------
       |MATERIAL|        | microhm-cm  |  Temp coef  | Temp Range  |    
---------------------------------------------------------------------
  Ni   |   Cr   |   Fe   |             |             |             
---------------------------------------------------------------------
 100   |   0    |   0    |     7.8     |             |     20C     | 
---------------------------------------------------------------------
  0    |  100   |   0    |     13      |             |     20C     |
---------------------------------------------------------------------
  0    |   0    |  100   |     10      |             |     20C     |
---------------------------------------------------------------------
  80   |   20   |   0    |     108     |   0.00011   |    20-500C  |
---------------------------------------------------------------------
  60   |   16   |   24   |     112     |   0.00015   |    20-500C  |
---------------------------------------------------------------------
  35   |   20   |   45   |     100     |   0.00036   |    20-500C  |
---------------------------------------------------------------------
 Inconel X (annealed)    |     122     | [m.p.1399C] |             |
---------------------------------------------------------------------
 Silver|        |        |    1.59     | [m.p. 960C] |     20C     |
--------------------------------------------------------------------

   In short, in can be seen that the relative electrical resistivity
 for nichrome to silver (in this simple matter) is: 


     rho (Nichrome)
     -------------    =  69.5   (average)
     rho  (silver)  

                          with a range of 62.89  to   76.73

  for this exercise.  Therefore, one can use 70 as an general ratio.

   How thin must a silver wire be, to equal the nichrome wire?  

   Hence a silver wire must be a little less than 1/8th the diameter
 of a nichrome wire to yield a relative area of 1/70th,  so as to insure
 an equivalent lumped parameter resistance, for an equal length of wire.

   Other length-area-resistivity problems are similarly calculated.

   Disclaimer: Of course, this ignores contact potentials, inhomogeneities,
        method of contacting said wire, surface vs. volume conductions, and 
        the impact of electric and magnetic fields, &tc.


     As for melting, the melting temperatures of the respective materials
 are listed in the Table above.   The next interested respondent 
 is welcome to estimate the thermal barriers surrounding this gendanken
 wire, given any putative applied (thermally dissipative) electrical load.
 
===================================================================
       Mitchell R. Swartz              JET Technology
       mica@world.std.com              (617) 239-8383

Newsgroups: sci.physics.fusion