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Thermal Properties of Matter — Physics STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 SciencePhysicsThermal Properties of Matter3 Marks
Question
Define coefficient of thermal conductivity. Derive its expression.
✓

Answer

Coefficient of thermal conductivity of a material is defined as the quantity of heat that flows in one second between the opposite faces of a cube of side $1 m$, the faces being kept at a temperature difference of $1^\circ C (or 1 K)$.Expression for coefficient of thermal conductivity:
  1. Under steady state condition, the quantity of heat ‘Q’ that flows from the hot face at temperature $T_1$ to the cold face at temperature $T_2$​​​​​​​ of a cube with side x and area of cross- section A is
    • directly proportional to the cross-sectional area A of the face. i.e.. $Q ∝ A$
    • directly proportional to the temperature difference between the two faces i.e., $Q ∝ (T_1 – T_2)$
    • directly proportional to time t (in seconds) for which heat flows i.e..$Q ∝ t$
    • inversely proportional to the perpendicular distance x between hot and cold faces i.e., $Q ∝ 1/x$
  2. Combining the above four factors, we have the quantity of heat
    $ Q \propto \frac{ A \left( T _1- T _2\right) t }{ x }$
    $\therefore Q =$
    where k is a constant of proportionality and is called coefficient of thermal conductivity. Its value depends upon the nature of the material.

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