Laraba na Wiedemann Franz

Wiedemann-Franz law yana da shari mai kula da thermal conductivity (κ) da electrical conductivity (σ) na zafi mai girma da ke da electrons da suka fitarwa da suka yi gaba-gaba a cikinsu.

• Thermal Conductivity (κ): Yana nuna (matsayin) adadin kayan mutum ya kai wani abu a tattara hawa.

• Electrical Conductivity (σ): Yana nuna (matsayin) adadin kayan mutum ya kai wani abu a tattara elektrik.

A fannin; idan tattalin hawa ta zama, zamaɗi na electrons da suka fitarwa ta zama, wanda yake buƙata da ziyarwa a tattara hawa, ko kuma ya buƙace maimaita daga ions da electrons da suka fitarwa. Wannan yana buƙata da electrical conductivity.

Shari yana bayyana tsarin al'adu da thermal conductivity ta zahiri a ciki a matsayin electrical conductivity ta zahiri (fanni) ta zama nasarar tattalin hawa.

Shari yana amsa da sunan Gustav Wiedemann da Rudolph Franz a shekarar 1853 suka tabbatar da tsarin al'aduyana da ma'anar sama a matsayin fannin daɗe a tattali hawa.

Derivation of the Law

Don haka, muna iya a faruwarwa a matsayin abu mai sanyi da mai girma. Abun yana a saukar da gradient na tattalin hawa. Tsarin tattarar hawa za a zama maki a tsohon gradient na tattalin hawa a kan abin da ke tattara.
Tsarin tattarar hawa a kan abin da ke tattara a lokacin da tattalin hawa ta zama flux. Yana zama nasarar gradient na tattalin hawa.

K → Coefficient of thermal conductivity (W/mK)
K = Kphonon + Kelectron; saboda tattarar hawa a solids yana ka phonon da electron.

Na gode, muna iya a faruwarwa a matsayin coefficient of thermal conductivity.
Don haka, muna iya a faruwarwa a matsayin tattarar hawa a matsayin tattalin hawa mai girma a cikin slab fanni da ke da gradient na tattalin hawa.

cv → Specific heat
n → Number of particles per unit volume
λ → mean free path of collisions
v → velocity of electrons

Duk da cewa an samu equations (1) da (2), muna iya samun

Muna sanin cewa energy of free electrons yana cewa

Muna ci equation (4) a (3)

Na gode, specific heat for an ideal gas at constant volume,

Idan muna ci equation (8) a (6), muna iya samun

Na gode, muna iya a faruwarwa a matsayin electrical current density of a metal with the application of electric field, E (figure 1)
J = σ E ; Ohms law


Saboda haka, form na daidai Ohms law yana ba da

Yana da mean free path and mean time between the collisions.

e → Charge of the electron = 1.602 × 10-9 C
τ → Collision time or mean time: It is the average time for the electron to move or travel prior to scattering.
vd → Drift Velocity: It is the standard velocity of the electron during the collision time.
When we put equation (11) in (10), we get electrical conductivity (Drude Conductivity) as

Consider the electrons which move in a metal without any application of electrical field. Then the equipartition theorem is given by

From equation (13) we get m as

Now, we put equation (14) in (12)