Why is thermal conductivity inversely proportional to temperature and relationship between molar conductivity and molar conductance?
The statement that thermal conductivity is inversely proportional to temperature is only partially true and depends on the specific material. Here's a breakdown:
Metals:
- In pure metals, thermal conductivity primarily relies on free electrons carrying heat. As temperature increases, the mean free path (average distance traveled by an electron before colliding with another particle) decreases. This increased collision frequency hinders efficient heat transfer, leading to a decrease in thermal conductivity with increasing temperature.
Non-metals:
- In non-metals, heat transfer involves lattice vibrations called phonons. At higher temperatures, increased phonon-phonon interactions cause more frequent collisions, similar to what happens in metals. This leads to a decrease in thermal conductivity with rising temperature.
However, it's important to note that:
- Not all materials exhibit this inverse relationship. In some, like water, thermal conductivity increases with temperature.
- The relationship between thermal conductivity and temperature can be complex and may involve different mechanisms depending on the material and temperature range.
Relationship between molar conductivity and molar conductance:
Molar conductivity (Λm) and molar conductance (Λ) are related by the formula:
Λm = Λ * (1000 / C)
where:
- Λm is molar conductivity in S cm²/mol (units of siemens per centimeter squared per mole)
- Λ is molar conductance in S cm²/mol (units of siemens per centimeter squared per mole)
- C is the concentration of the solution in mol/L (moles per liter)
Molar conductivity represents the conductivity per mole of solute in a solution, while molar conductance refers to the conductivity per mole of electrolyte at a specific concentration. They are essentially different ways to express the same underlying concept, with molar conductivity accounting for the number of moles of solute present.
I hope this clarifies the relationship between thermal conductivity and temperature for different materials and the connection between molar conductivity and molar conductance!
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