# Electrical & Thermal Conductivity and Wiedemann Franz Law

By | September 3, 2018

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 20oC

 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

### Discover more from Electrical Engineering 123

Subscribe to get the latest posts sent to your email.