Temperature dependence of the electrical resistivity of a metal

In summary: T is the absolute temperature in the range near room temperature or above, where classical statistical mechanics can validly be applied to discuss the vibrations of the atoms in the metals. In summary, the electrical resistivity ρ of a metal is dependent on the probability of electron scattering and the mean square amplitude of vibration of the atoms in the lattice. This probability is in turn proportional to the absolute temperature, as stated by the equipartition theorem. Therefore, the electrical resistivity ρ is directly proportional to the absolute temperature in the range near room temperature or above, where classical statistical mechanics can be applied to study the vibrations of the atoms in metals.
  • #1
ayazdipour
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the electrical resistivity ρ of a metal is proportional to the probability that an electron is seattered by the vibrating atoms in the lattice an this probability is in turn proportional to the mean square amplitude of vibration of these atoms.How dose the electrical resistivity ρ of the metal depend on its absolute temperature in the range near room temperature or above where classical statistical mechanics can validly be applied to discuss the vibrations of the atomes in the metals?
 
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  • #2
ayazdipour said:
the electrical resistivity ρ of a metal is proportional to the probability that an electron is seattered by the vibrating atoms in the lattice an this probability is in turn proportional to the mean square amplitude of vibration of these atoms.How dose the electrical resistivity ρ of the metal depend on its absolute temperature in the range near room temperature or above where classical statistical mechanics can validly be applied to discuss the vibrations of the atomes in the metals?

a indicated by problem . the electrical resistivity ρ of a metal is proportional to the probability ρ that an electron is scattrered by the vibrating atoms in the lattice and this probability ρ is proportional to the mean square amplitude of vibration of these atoms <A^2> since <A^2> is proportional to the average of potential energy energy <Ep>.which is proportional to T due to equipartition theorem .thus the electrical resistivity ρ is proportional to T
 

1. What is the electrical resistivity of a metal?

The electrical resistivity of a metal is a measure of how strongly a material opposes the flow of electric current. It is typically represented by the Greek letter rho (ρ) and is measured in units of ohm-meters (Ω·m).

2. What factors affect the temperature dependence of electrical resistivity in metals?

The temperature dependence of electrical resistivity in metals is affected by factors such as the metal's composition, crystal structure, and impurities. Other factors such as the strength of the metal's electron-phonon interactions and the presence of magnetic or superconducting properties can also influence its temperature dependence.

3. How does temperature affect the electrical resistivity of a metal?

As temperature increases, the electrical resistivity of a metal typically increases as well. This is due to the increased thermal vibrations of the metal's atoms, which disrupt the flow of electrons and increase the resistance to current flow.

4. Is there a specific pattern or relationship between temperature and electrical resistivity in metals?

Yes, the temperature dependence of electrical resistivity in metals can often be described by a power law relationship, where the resistivity (ρ) is proportional to the temperature (T) raised to a certain exponent (n): ρ ∝ T^n. This exponent can vary depending on the metal's properties and temperature range.

5. How is the temperature dependence of electrical resistivity measured in metals?

The temperature dependence of electrical resistivity in metals is typically measured by conducting experiments where the resistivity of the metal is measured at different temperatures. This data can then be analyzed to determine the relationship between temperature and resistivity and to calculate the exponent (n) in the power law equation.

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