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 |