Thermal conduction is the process of heat transfer through direct contact between particles within a substance, particularly in solids(except Hg). It occurs due to the exchange of kinetic energy between neighboring particles, resulting in the transfer of heat energy from regions of higher temperature to regions of lower temperature. In thermal conduction, the particles themselves do not significantly move from their positions; instead, their vibrations and collisions lead to the propagation of heat energy throughout the material. Heat transfer by conduction from one part of body to another continues till their temperatures become equal.
For example if you hold an iron rod with one of its end on a fire for some time, the handle will get hot. The heat is transferred from the fire to the handle by conduction along the length of iron rod. The vibrational amplitude of atoms and electrons of the iron rod at the hot end takes on relatively higher values due to the higher temperature of their environment. These increased vibrational amplitude are transferred along the rod, from atom to atom during collision between adjacent atoms. In this way a region of rising temperature extends itself along the rod to your hand.
Steady State and Variable State
Variable State :- When heat is supplied to one end of a metallic rod, each cross-section of the rod gains or absorbs heat & passes the rest of the heat to the next cross-section.
Heat received by each cross-section of the rod from hotter end used in three ways :-
(i) A part of heat is absorbed by the cross-section, which increases it’s temperature.
(ii) Another part is transferred to the neighboring cross-section &
(iii) Remaining part radiates into atmosphere.
The state of the rod in which each cross-section absorbs heat and temperature of each cross-section is not constant, is called variable state.
Steady State :- If the temperature of a cross-section at any position x in a rod, remains constant with time (remember, it does vary with position x), the rod is said to be in steady state.
For a conductor to be in steady state, there is no absorption or emission of heat at any cross-section. (as temperature at each point remains constant with time). The left and right faces are maintained at constant temperatures TH and TL respectively, and all other faces must be covered with adiabatic walls so that no heat escapes through them by radiation and same amount of heat flows through each cross-section in a given interval of time. In this state, the heat that reaches any cross-section is transmitted to the next cross-section.