Conduction - Thermal Conductivity

Thermal conductivity of a solid is a measure of the ability of the solid to conduct heat through it. Thus, good conductors of heat have higher thermal conductivity than bad conductors.

Under steady state condition, the temperature at points within the rod decreases uniformly with distance from the hot end to the cold end. The fall of temperature with distance between the ends of the rod in the direction of flow of heat is called the temperature gradient.

\[\frac {(T_1-T_2)}{x}\]

where,

• T₁ = Temperature of hot end
• T₂ = Temperature of cold end
• x = Length of the rod

Suppose one end of a metal rod is heated. The heat flows by conduction from the hot end to the cold end. As a result, the temperature of every section of the rod starts increasing. The rod is said to be in a variable temperature state.

After some time, the temperature at each section of the rod becomes steady – i.e., it does not change. Note that the temperature of each cross-section of the rod is constant but not the same. This is called the 'steady-state condition'.

Fig.: Metal rod heated at one end. Heat flows from hot end (T₁) to cold end (T₂). In steady state, temperature decreases uniformly from T₁ to T₂ along the length.

1. Variable Temperature State
   When one end of the rod is first heated, the temperature of every section of the rod keeps increasing with time. The system is still adjusting. The rod is said to be in a variable temperature state.
2. Steady-State Condition

   After some time, the temperature at each section becomes steady (does not change with time). The temperature at each cross-section isconstant but not the same across different sections. This is called the steady-state condition.

Fig.: Variable Temperature State (left) — The temperatures of all sections are still rising. Steady State (right) — temperatures are fixed at each section but different across the rod.

• Thermal conductivity is the measure of a solid's ability to conduct heat. Good conductors have higher thermal conductivity.
• When a metal rod is heated at one end, heat flows from the hot end to the cold end by conduction.
• Variable state — the temperature of every section keeps increasing with time.
• Steady state — temperature at each section is constant but different across sections.
• Temperature gradient = (T₁ − T₂) / x — the fall of temperature per unit length in the direction of heat flow.