Electrical & Thermal Conductivity and Wiedemann Franz Law

Conductivity refers to the ability to conduct, convey or pass through, and in case of electricity it refers to ability to convey the electric current. On the other hand for thermal conductivity it is the ability to conduct or pass the heat for any material.

Similarly if we talk about the reverse side of conductivity it becomes the resistivity, which means how much a material is resistive to the flow of current or flow of heat.

Different materials are having different electrical and thermal conductivity values that determines whether it is easy or difficult to transfer the current or heat. Obviously if resistance is high we will need much power or heat to transfer same amount of electricity or heat as compared to other material with less resistance.

Formula for Electrical Conductivity

This is obvious that if we increase the length of conductor conductivity will reduce since electrons need to travel more and face more resistive forces. Therefore conductance or conductivity is inversely proportional to length of the conductor. Therefore

G ∝ 1/l    equation (1)

Similarly if cross sectional area of conductor is increased then current gets more drift electrons. Hence, conductance of the conductor increases. Therefore

G ∝ A     equation (2)

From equation (1) and (2),

G ∝ A/l and 

G = σ A/l

Where, σ = constant of proportional known as conductivity or specific conductance.

Formula for Thermal Conductivity

Let us consider a block of material with one end at temperature T₁ and other at T₂. As per the Fourier Law heat flows from high temperature to low temperature. Therefore for T₁>T₂, heat flows from T₁ end to T₂ end, and the heat flux(J) flowing across a unit area per unit time is given as:

Where, K is the thermal conductivity in Joule/meter-sec-K or Watts/meter-K.

Relationship of Electrical & Thermal Conductivity – Wiedemann Franz Law

Gustav Wiedemann and Rudolph Franz in 1853 found the relationship between electrical and thermal conductivity and presented the law known as Wiedemann Franz Law that states that the ration of both properties is more or less the similar value for dissimilar metal at the same temperature.

It also stated that once we increase the temperature of a metal its thermal conductivity increases but its electrical conductivity decreases.

The law defines the ratio of the electronic role of the thermal conductivity of a material to the electrical conductivity of a material (metal) is directly relative to the temperature.

Table of Resistivity and Conductivity of Different Materials at 20^oC

Material	Resistivity at 20oC	Conductivity 20oC
Air	1.3 × 1016 to 3.3 × 1016	3 × 10-15 to 8 × 10-15
Aluminum	2.82 × 10-8	3.5 × 107
Annealed copper	1.72 × 10-8	5.80 × 107
Calcium	3.36 × 10-8	2.98 × 107
Carbon (amorphous)	5 × 10-4 to 8 × 10-4	1.25 to 2 × 103
Carbon (diamond)	1 × 1012	~10-13
Carbon (graphite)	2.5 × 10-6 to 5.0 × 10-6 //basal plane	2 to 3 × 105 //basal plane
Carbon steel	-1010	1.43 × 10-7
Constantan	4.9 × 10-7	2.04 × 106
Copper	1.68 × 10-8	5.96 × 107
Deionized water	1.8 × 105	5.5 × 10-6
Drinking water	2 × 101 to 2 × 103	5 × 10-4 to 5 × 10-2
Fused quartz	7.5 × 1017	1.3 × 10-18
GaAs	5 × 10-7 to 10 × 10-3	5 × 10-8 to 103
Germanium	4.6 × 10-1	2.17
Glass	10 × 1010 to 10 × 1014	10-11 to 10-15
Gold	2.44 × 10-8	4.10 × 107
Grain oriented electrical steel	4.60 × 10-7	2.17 × 106
Hard rubber	1 × 1013	10-14
Iron	1.0 × 10-7	1.00 × 107
Lead	2.2 × 10-7	4.55 × 106
Lithium	9.28 × 10-8	1.08 × 107
Manganin	4.82 × 10-7	2.07 × 106
Mercury	9.8 × 10-7	1.02 × 106
Nichrome	1.10 × 10-6	9.09 × 105
Nickel	6.99 × 10-8	1.43 × 107
Paraffin wax	1 × 1017	10-18
PET	10 × 1020	10-21
Platinum	1.06 × 10-7	9.43 × 106
Sea water	2 × 10-1	4.8
Silicon	6.40 × 102	1.56 × 10-3
Silver	1.59 × 10-8	6.30 × 107
Stainless steel	6.9 × 10-7	1.45 × 106
Sulfur	1 × 1015	10-16
Teflon	10 × 1022 to 10 × 1024	10-25 to 10-23
Tin	1.09 × 10-7	9.17 × 106
Titanium	4.20 × 10-7	2.38 × 106
Tungsten	5.60 × 10-8	1.79 × 107
Wood (damp)	1 × 103 to 4	10-4 to 10-3
Wood (oven dry)	1 × 1014 to 16	10-16 to 10-14
Zinc	5.90 × 10-8	1.69 × 107