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प्रश्न
Answer the following question.
Derive its expression for the coefficient of thermal conductivity.
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उत्तर
The expression for coefficient of thermal conductivity:
- Under steady state condition, the quantity of heat ‘Q’ that flows from the hot face at temperature T1 to the cold face at temperature T2 of a cube with side x and area of crosssection 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 ∝ (T1 - T2)
- 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
Combining the above four factors, we have the quantity of heat
`"Q" prop ("A"("T"_1 - "T"_2)"t")/"x"`
∴ `"Q" = ("kA"("T"_1 - "T"_2)"t")/"x"`
where k is a constant of proportionality and is called the coefficient of thermal conductivity. Its value depends upon the nature of the material.
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