Question

If \( K \) and \( \sigma \) be the thermal and electrical conductivities of a metal at temperature \( T \), then

• A. \( \frac{KT}{\sigma} = \text{constant} \)
• B. \( \frac{K\sigma}{T} = \text{constant} \)
• C. \( \frac{\sigma}{KT} = \text{constant} \)
• D. \( \frac{K}{\sigma T} = \text{constant} \)

Hint:

The Wiedemann-Franz Law explains the direct proportionality between thermal and electrical conductivities in metals, governed by the \textbf{Lorenz number}.

Answer 1

The Correct Option is A

The relationship between thermal conductivity (\( K \)) and electrical conductivity (\( \sigma \)) in metals is governed by the Wiedemann-Franz Law, which states: \[ \frac{K}{\sigma T} = L \] where: - \( K \) is the thermal conductivity, - \( \sigma \) is the electrical conductivity, - \( T \) is the absolute temperature, - \( L \) is the Lorenz number, a fundamental constant. Step 1: Rearranging the Wiedemann-Franz Law Multiplying both sides by \( T \), we get: \[ \frac{KT}{\sigma} = L \times T \] Since \( L \) is a constant, the equation simplifies to: \[ \frac{KT}{\sigma} = \text{constant}. \]


Step 2: Evaluating the Options - Option (A) - Correct: This matches the rearranged form of Wiedemann-Franz Law. - Option (B) - Incorrect: The product \( K\sigma \) divided by \( T \) is not a fundamental constant. - Option (C) - Incorrect: The reciprocal form \( \frac{\sigma}{KT} \) does not hold according to the Wiedemann-Franz Law. - Option (D) - Incorrect: \( \frac{K}{\sigma T} = \text{constant} \) is incorrect, as it should be \( \frac{KT}{\sigma} \).


Step 3: Conclusion Since the correct form derived from Wiedemann-Franz Law is \( \frac{KT}{\sigma} = \text{constant} \), the correct answer is option (A).