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Conduction - Lesson Summary

There are three different modes by which “heat” transfer takes place. They are thermal conduction, convection, and radiation.
Thermal conduction is a mechanism of heat transfer between two adjacent parts of a body, or between two bodies in thermal contact, because of their temperature difference.

For example, a person holding an iron rod at one end and placing the other end in fire.
One end of the iron rod, which is in flame; is at high temperature and the other end is at low temperature.
Heat flows from hot end to cold end by “ thermal conduction”, and as a result, after some time the person drops the rod. 
The molecules at hotter regions have more kinetic energy. A part of their energy is parted to its neighbouring molecules; those neighbouring molecules will in turn pass it to its other neighbours.

Thermal conductivity of a substance, which most often is also referred to as conductivity, depends on the state and nature of the substance.
In solids, metals are very good conductors of heat. The free electrons of metals help transfer of heat energy very quickly.
Gases are very bad conductors of heat. The conductivity of liquids lies between the conductivities of solids and gases.
Now, consider a metallic rod of length “L” and cross sectional area “A”.
Let the two ends of the rod be maintained at two different constant temperatures, T 1 and T 2, with T 1 greater than T 2 by keeping them in thermal contact with two reservoirs at the corresponding constant temperatures. Thus, the end of the rod where the temperature is T 1 is the hot end and the other end is the cold one.
Let us also assume that the rod is fully insulated and there is no loss of heat to surroundings.
Heat starts flowing from hot end to cold end, and after some time there will be a steady flow of heat through the rod.
“Heat current” is defined as the rate of heat flow. If “dQ” is the heat flowing in “dt” time, then “heat current  H = dQ/dt 
In steady state, the temperature of the rod decreases uniformly from hot to cold end of the rod and the change in temperature per unit length is defined as “temperature gradient”
If “dT” is the change in temperature for a length of “dl” then, Temperature gradient = dT/dl   It is experimentally found that, in steady state, heat current, H, is directly proportional to the temperature difference between the two ends, and cross sectional area of the rod. It is also found that “H” is inversely proportional to the length of the rod.
Where “k” is the proportionality constant and is called “thermal conductivity” of the material.
The SI unit of thermal conductivity is joule per second per metre per kelvin; “J s -1 m -1 K -1” or watt per metre per kelvin; “W m -1 K -1
Metals have very high thermal conductivities and hence conduct heat rapidly.
Materials like wood are bad conductors.
When heat flow is to be restricted, the body must be surrounded by an insulating substance.
For example, people use woollen cloths in winter to prevent loss of heat as the air entrapped in the pores of wool fabric acts like an insulator.
When heat flow is required, good conductors are used.
For example, cooking utensils, water coolant systems in car radiators and nuclear power plants all are use good conductors.


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