ܒܝܛܐ ܬܪܡܘܕܝܢܡܝܩܝܬܐ

ܣܩܵܠܵܐ ܕܡܫܲܚܠܦܵܢܘܼܬ݂ܵܐ ܕܛܶܡܦܸܪܲܛܘܼܪܵܐ/ܩܪܝܪܘܬܐ ܒܛܥ"ܚ: ܛܶܡܦܸܪܲܛܘܼܪ̈ܵܬ݂ܵܐ ܒܣܩܵܠܵܐ ܕܩܹܠܒ݂ܝܼܢ ܚܘܼܘܵܝܹ̈ܐ ܝܢܵܐ ܒܓܵܘܢܵܐ ܙܪܘܩܐ (ܣܩܵܠܵܐ ܕܨܹܠܣܝܘܼܣ — ܒܝܲܪܘܿܩܵܐ، ܣܩܵܠܵܐ ܕܦܵܪܹܢܗܵܝܛ — ܒܣܘܼܡܵܩܵܐ)، ܫܘܘ̈ܝܵܐ ܕܩܪܝܪܘܬܐ ܒܓܝܼܓܵܒ݂ܵܝܛ ܠܟܠ ܢܵܢܘܿܓ'ܘܼܠ ܚܘܼܘܵܝܹ̈ܐ ܝܢܵܐ ܒܐܘܼܟܵܡܵܐ. ܛܶܡܦܸܪܲܛܘܼܪܵܐ ܠܵܐ-ܣܟ݂ܵܝܬ݂ܵܐ (ܩܪܝܪܘܬܐ ܕܨܦܪ) ܚܘܼܘܵܝܬ݂ܵܐ ܝܠܵܗ̇ ܒܥܸܠܵܝ ܣܘܼܪܛܵܐ؛ ܫܘܘ̈ܝܵܐ ܚܲܝܘܼܒ݂ܵܝܹ̈ܐ ܕܩܪܝܪܘܬܐ/ܛܶܡܦܸܪܲܛܘܼܪܵܐ — ܡ̣ܢ ܝܲܡܝܼܢܵܐ، ܣܲܩܘܼܒ݂ܠܵܝܹ̈ܐ — ܡ̣ܢ ܣܸܡܵܠܵܐ.

ܒܬܪܡܘܕܝܢܡܝܩܐ ܣܛܲܛܝܼܣܛܝܼܬ݂ܵܐ ܒܹܝܛܵܐ ܬܪܡܘܕܝܢܡܝܩܝܬܐ, ܐܝܼܕ݂ܝܼܥܬܵܐ ܐܘܼܦ ܐܲܝܟ݂ ܩܪܝܪܘܬܐ, ܗܝܼܝܘ ܓܵܘܵܐ ܗܦܝܼܟ݂ܵܐ ܕܛܶܡܦܸܪܲܛܘܼܪܵܐ ܬܪܡܘܕܝܢܡܝܩܝܬܐ ܕܛܲܟ݂ܣܵܐ:$$\beta ={\frac {1}{k_{\rm {B}}T}}$$ (ܐܲܝܟܵܐ ܕ T ܝܠܵܗ̇ ܛܶܡܦܸܪܲܛܘܼܪܵܐ، ܘ k_B ܝܠܹܗ ܩܘܝܡܐ ܕܒܘܠܨܡܢ).

ܒܹܝܛܵܐ ܬܪܡܘܕܝܢܡܝܩܝܬܐ ܐܝܼܬ ܠܵܗ̇ ܓܲܒ݂ܵܐ ܗܦܝܼܟ݂ܵܐ ܕܐܹܢܹܪܓܝܼܵܐ (ܒܚܕ̈ܘܬܐ ܕܛܥ"ܚ، ܓ'ܘܼܠ ܗܦܝܼܟ݂ܵܐ، $[\beta ]={\textrm {J}}^{-1}$). ܒܚܕ̈ܘܬܐ ܠܵܐ-ܚܲܡܝܼܡܵܝܹ̈ܐ، ܡܵܨܝܵܐ ܐܘܼܦ ܠܡܬܬܟ݂ܵܫܵܐ ܒܒܵܝܛܹ̈ܐ ܠܟܠ ܓ'ܘܼܠ، ܐܲܘ ܒܕܵܐܟ݂ܝܼ ܦܫܝܼܩܘܼܬ݂ܵܐ، ܒܓܝܼܓܵܒ݂ܵܝܛܹ̈ܐ ܠܟܠ ܢܵܢܘܿܓ'ܘܼܠ؛ 1 K⁻¹ ܫܲܘܝܵܐ ܝܠܹܗ ܐܲܝܟ݂ 13,062 ܓܝܼܓܵܒ݂ܵܝܛܹ̈ܐ ܠܟܠ ܢܵܢܘܿܓ'ܘܼܠ؛ ܒܛܶܡܦܸܪܲܛܘܼܪܵܐ ܕܐܲܬ݂ܪܵܐ: T = 300 K, β ≈ 44 ܓܒ/ܢܓ' ≈ 39 ܐܒ⁻¹ ≈ 2.4×10²⁰ ܓ'⁻¹. ܡܵܢܝܵܢܵܐ ܕܡܫܲܚܠܦܵܢܘܼܬ݂ܵܐ: 1 ܓܒ/ܢܓ' = $8\ln 2\times 10^{18}$ ܓ'⁻¹.

ܫܘܼܘܕܵܥܵܐ

ܒܹܝܛܵܐ ܬܪܡܘܕܝܢܡܝܩܝܬܐ، ܒܓܵܘܗ̇، ܝܠܵܗ̇ ܐܣܵܪܵܐ ܡܚܲܒܪܵܢܵܐ ܒܹܝܬ ܦܘܠܚܢܐ ܕܝܕ̈ܥܬܐ ܘܡܟܢܝܩܘܬܐ ܣܛܲܛܝܼܣܛܝܼܬ݂ܵܐ ܒܦܘܼܫܵܩܵܐ ܕܛܲܟ݂ܣܵܐ ܦܝܼܙܝܼܩܵܝܵܐ ܒܝܲܕ ܐܢܛܪܘܦܝܐ ܕܝܼܹܗ ܘܬܪܡܘܕܝܢܡܝܩܐ ܐܣܝܼܪܬܵܐ ܒܐܢܪܓܝܐ ܕܝܼܹܗ. ܗ̇ܝ ܡܲܒܝܸܢܵܐ ܦܘܼܢܵܝܵܐ ܕܐܢܛܪܘܦܝܐ ܠܡܲܣܩܵܢܘܼܬ݂ܵܐ ܕܐܢܪܓܝܐ. ܐܸܢ ܟܡܵܝܘܼܬ݂ܵܐ ܙܥܘܿܪܬܵܐ ܕܐܢܪܓܝܐ ܡܲܘܣܸܦܵܐ ܠܛܲܟ݂ܣܵܐ، β ܡܲܫܡܸܗܵܐ ܕܲܪܓ݂ܵܐ ܕܥܠܝܼܒ݂ܵܝܘܼܬ݂ܵܐ ܕܛܲܟ݂ܣܵܐ.

ܒܝܲܕ ܣܘܼܘܕܵܥܵܐ ܣܛܲܛܝܼܣܛܝܼܩܵܝܵܐ ܕܛܶܡܦܸܪܲܛܘܼܪܵܐ ܐܲܝܟ݂ ܦܘܼܠܚܵܢܵܐ ܕܐܢܛܪܘܦܝܐ، ܦܘܼܠܚܵܢܵܐ ܕܩܪܝܪܘܬܐ ܡܵܨܝܵܐ ܠܡܬܚܲܫܒ݂ܵܢܵܐ ܒܟܢܘܫܝܐ ܡܝܟܪܘ-ܟܢܘܢܝܐ ܒܦܘܼܪܡܘܼܠܵܐ

$\beta ={\frac {1}{k_{\rm {B}}T}},={\frac {1}{k_{\rm {B}}}}\left({\frac {\partial S}{\partial E}}\right)_{V,N}$

(ܐܲܝܢܘ ܕܝܢ، ܦܘܠܓܐ ܦܠܝܓܝܐ ܕܐܢܛܪܘܦܝܐ S ܠܦܘܼܬ݂ ܐܢܪܓܝܐ E ܒܫܘܦܥܐ ܩܲܝܵܡܵܐ V ܘܡܸܢܝܵܢܵܐ ܕܦܪ̈ܕܐ N).

ܫܘܼܘܟ݂ܵܢܹ̈ܐ

ܐܦܸܢ β ܫܲܠܡܵܐܝܼܬ ܫܲܘܝܵܐ ܝܠܵܗ̇ ܠܛܶܡܦܸܪܲܛܘܼܪܵܐ ܒܡܵܘܗܲܒ݂ܬܵܐ ܪܸܢܝܵܢܵܝܬܵܐ، ܓܵܠܝܼܒ݂ܵܐܝܼܬ ܡܸܬܚܲܫܒ݂ܵܐ ܓܵܘܵܐ ܝܲܬܝܼܪ ܫܹܪܫܵܝܵܐ ܡ̣ܢ ܛܶܡܦܸܪܲܛܘܼܪܵܐ، ܡܸܛܠ ܓܸܕܫܵܐ ܕܛܶܡܦܸܪܲܛܘܼܪܵܐ ܣܲܩܘܼܒ݂ܠܵܝܬܵܐ، ܕܒܹܗ β ܐܡܝܼܢܵܝܬܵܐ ܝܠܵܗ̇ ܟܲܕ ܥܵܒ݂ܪܵܐ ܒܨܸܦܪ، ܒܥܸܕܵܢܵܐ ܕ T ܐܝܼܬ ܠܵܗ̇ ܝܼܚܝܼܕܵܝܘܼܬ݂ܵܐ.

ܢܘܼܣܵܦ ܥܲܠ ܗܵܕܹܐ، β ܐܝܼܬ ܠܵܗ̇ ܫܘܼܘܟ݂ܵܢܵܐ ܕܐܣܵܪܵܗ̇ ܥܸܠܬܵܢܵܝܵܐ-ܡܲܦܩܵܢܵܝܵܐ ܝܲܬܝܼܪ ܦܫܝܼܩ ܝܠܹܗ ܠܡܸܣܬܲܟ݁ܵܠܘܼܗܝ: ܐܸܢ ܟܡܵܝܘܼܬ݂ܵܐ ܙܥܘܿܪܬܵܐ ܕܚܘܼܡܵܐ ܡܲܘܣܸܦܵܐ ܠܛܲܟ݂ܣܵܐ، β ܓܲܠܡܵܐ ܡܲܣܩܵܢܘܼܬ݂ܵܐ ܕܐܢܛܪܘܦܝܐ ܦܠܝܼܓܬܵܐ ܥܲܠ ܡܲܣܩܵܢܘܼܬ݂ܵܐ ܕܚܘܼܡܵܐ. ܛܶܡܦܸܪܲܛܘܼܪܵܐ ܩܲܫܝܵܐ ܝܠܵܗ̇ ܠܡܦܲܫܵܩܵܗ̇ ܒܗܲܪ ܗܵܢܵܐ ܣܘܼܟܵܠܵܐ، ܡܸܛܠ ܕܠܲܝܬ ܐܸܡܟܵܢ "ܠܡܲܘܣܵܦܹܐ ܐܢܛܪܘܦܝܐ" ܠܛܲܟ݂ܣܵܐ ܐܸܠܵܐ ܐܸܢ ܒܐܘܼܪܚܵܐ ܥܩܝܼܡܬܵܐ، ܒܝܲܕ ܡܫܲܚܠܵܦܘܼ ܓܵܘܹ̈ܐ ܐܚܹܪ̈ܢܹܐ، ܐܲܝܟ݂ ܛܶܡܦܸܪܲܛܘܼܪܵܐ، ܫܘܦܥܐ ܐܲܘ ܡܸܢܝܵܢܵܐ ܕܦܪ̈ܕܐ.

ܦܘܼܫܵܩܵܐ ܣܛܲܛܝܼܣܛܝܼܩܵܝܵܐ

ܡ̣ܢ ܓܹܒܵܐ ܣܛܲܛܝܼܣܛܝܼܩܵܝܵܐ، β — ܝܠܵܗ̇ ܓܵܘܵܐ ܡܸܢܝܵܢܵܝܵܐ ܕܐܵܣܿܪ ܬܪܹܝܢ ܛܲܟ݂ܣܹ̈ܐ ܡܲܩܪܘܿܣܩܘܿܦܵܝܹ̈ܐ ܒܫܲܘܝܘܼܬ ܡܲܬܟ݁ܠܵܐ. ܦܘܼܪܡܘܼܠܵܐ ܓܲܫܡܵܝܵܐ ܗܵܢܵܘ. ܚܵܫܒ݂ܲܚ ܬܪܹܝܢ ܛܲܟ݂ܣܹ̈ܐ، 1 ܘ-2، ܒܐܣܵܪܵܐ ܚܲܡܝܼܡܵܝܵܐ، ܥܲܡ ܐܢܪ̈ܓܝܵܬ݂ܵܐ ܕܝܼܠܲܝܗܝ E₁ ܘ-E₂. ܢܣܲܒܪܲܚ ܕE₁ + E₂ = ܚܲܕ ܩܲܝܵܡܵܐ E. ܡܸܢܝܵܢܵܐ ܕܡܝܟܪܘ-ܐܘܟܝ̈ܬܐ ܕܟܠ ܛܲܟ݂ܣܵܐ ܢܲܫܡܲܗ Ω₁ ܘ-Ω₂. ܒܣܘܼܒܵܪ̈ܲܢ، Ω_i ܬܠܝܼܬ݂ܵܐ ܝܠܵܗ̇ ܒܠܚܘܿܕ ܒ-E_i. ܢܣܲܒܪܲܚ ܐܘܼܦ ܕܟܠ ܡܝܟܪܘ-ܐܘܟܝܬܐ ܕܛܲܟ݂ܣܵܐ 1 ܕܫܠܝܼܡܵܐ ܥܲܡ E₁، ܡܵܨܝܵܐ ܠܡܸܬܩܲܝܵܡܘܼ ܥܲܡ ܟܠ ܡܝܟܪܘ-ܐܘܟܝܬܐ ܕܛܲܟ݂ܣܵܐ 2 ܕܫܠܝܼܡܵܐ ܥܲܡ E₂. ܒܕܵܐܟ݂ܝܼ، ܡܸܢܝܵܢܵܐ ܕܡܝܟܪܘ-ܐܘܟܝ̈ܬܐ ܕܛܲܟ݂ܣܵܐ ܡܚܲܝܕܵܐ ܝܠܹܗ

$\Omega =\Omega _{1}(E_{1})\Omega _{2}(E_{2})=\Omega _{1}(E_{1})\Omega _{2}(E-E_{1}).,$

ܒܸܬ ܢܲܦܩܲܚ β ܡ̣ܢ ܝסܘܕܐ ܪܫܝܐ ܕܡܟܢܝܩܐ ܣܛܛܝܣܛܝܩܝܬܐ:

ܟܲܕ ܛܲܟ݂ܣܵܐ ܡܚܲܝܕܵܐ ܡܵܛܹܐ ܠܫܲܘܝܘܼܬ ܡܲܬܟ݁ܠܵܐ، ܡܸܢܝܵܢܵܐ Ω ܡܸܬܡܲܪܒܹܐ.

(ܒܡܸܠܹ̈ܐ ܐܚܹܪ̈ܢܹܐ، ܛܲܟ݂ܣܵܐ ܟܝܵܢܵܐܝܼܬ ܓܵܪܹܫ ܠܡܸܢܝܵܢܵܐ ܡܲܪܒܵܢܵܐ ܕܡܝܟܪܘ-ܐܘܟܝ̈ܬܐ.) ܒܕܵܐܟ݂ܝܼ، ܒܫܲܘܝܘܼܬ ܡܲܬܟ݁ܠܵܐ:

${\frac {d}{dE_{1}}}\Omega =\Omega _{2}(E_{2}){\frac {d}{dE_{1}}}\Omega _{1}(E_{1})+\Omega _{1}(E_{1}){\frac {d}{dE_{2}}}\Omega _{2}(E_{2})\cdot {\frac {dE_{2}}{dE_{1}}}=0.$

ܐܸܠܵܐ E₁ + E₂ = E ܣܵܗܹܕ:

${\frac {dE_{2}}{dE_{1}}}=-1.$

ܗܵܕܟ݂ܵܐ

$\Omega _{2}(E_{2}){\frac {d}{dE_{1}}}\Omega _{1}(E_{1})-\Omega _{1}(E_{1}){\frac {d}{dE_{2}}}\Omega _{2}(E_{2})=0$

ܐܲܝܢܘ ܕܝܢ،

${\frac {d}{dE_{1}}}\ln \Omega _{1}={\frac {d}{dE_{2}}}\ln \Omega _{2}\quad {\mbox{ܒܫܲܘܝܘܼܬ ܡܲܬܟ݁ܠܵܐ.}}$

ܐܣܵܪܵܐ ܕܠܥܸܠ ܓܵܪܹܫ ܣܘܼܘܕܵܥܵܐ ܕβ:

$\beta ={\frac {d\ln \Omega }{dE}}.$

ܐܣܵܪܵܐ ܒܹܝܬ ܦܘܼܫܵܩܹ̈ܐ ܣܛܲܛܝܼܣܛܝܼܩܵܝܹ̈ܐ ܘܬܪܡܘܕܝܢܡܝܩܵܝܹ̈ܐ

ܟܲܕ ܬܪܹܝܢ ܛܲܟ݂ܣܹ̈ܐ ܐܝܼܬܲܝܗܘܿܢ ܒܫܲܘܝܘܼܬ ܡܲܬܟ݁ܠܵܐ، ܐܝܼܬ ܠܗܘܿܢ ܗܲܪ ܗ̇ܝ ܛܶܡܦܸܪܲܛܘܼܪܵܐ ܬܪܡܘܕܝܢܡܝܩܝܬܐ T. ܒܕܵܐܟ݂ܝܼ، ܪܸܢܝܵܢܵܐܝܼܬ ܢܸܣܒܲܪ ܕβ (ܕܡܘܼܕܥܬܵܐ ܒܝܲܕ ܡܝܟܪܘ-ܐܘܟܝ̈ܬܐ) ܐܣܝܼܪܵܐ ܝܠܵܗ̇ ܒܐܘܼܪܚܵܐ ܡܸܢܕܝܼ ܥܲܡ T. ܗܵܢܵܐ ܐܣܵܪܵܐ ܡܸܬܝܲܗܒ݂ܵܐ ܒܝܲܕ ܝְܣܘܿܕ݂ܵܐ ܪܫܵܝܵܐ ܕܒܘܿܠܨܡܲܢ، ܟܬܝܼܒ݂ܵܐ ܐܲܝܟ݂

$S=k_{\rm {B}}\ln \Omega ,$

ܐܲܝܟܵܐ ܕk_B ܝܠܹܗ ܩܘܝܡܐ ܕܒܘܠܨܡܢ، S ܝܠܵܗ̇ ܐܢܛܪܘܦܝܐ ܬܪܡܘܕܝܢܡܝܩܝܬܐ ܩܠܵܣܝܼܩܵܝܬܵܐ، ܘ Ω ܝܠܹܗ ܡܸܢܝܵܢܵܐ ܕܡܝܟܪܘ-ܐܘܟܝ̈ܬܐ. ܒܕܵܐܟ݂ܝܼ،

$d\ln \Omega ={\frac {1}{k_{\rm {B}}}}dS.$

ܒܡܲܥܒ݂ܵܪܵܐ ܠܣܘܼܘܕܵܥܵܐ ܕβ ܡ̣ܢ ܣܘܼܘܕܵܥܵܐ ܣܛܲܛܝܼܣܛܝܼܩܵܝܵܐ ܕܠܥܸܠ، ܩܵܒܠܲܚ

$\beta ={\frac {1}{k_{\rm {B}}}}{\frac {dS}{dE}}.$

ܒܦܘܼܚܵܡܵܐ ܥܲܡ ܦܘܼܪܡܘܼܠܵܐ ܬܪܡܘܕܝܢܡܝܩܝܬܐ

${\frac {dS}{dE}}={\frac {1}{T}},$

ܐܝܼܬ ܠܲܢ

$\beta ={\frac {1}{k_{\rm {B}}T}}={\frac {1}{\tau }}$

ܐܲܝܟܵܐ ܕ$\tau$ ܡܸܬܩܲܪܝܵܐ ܛܶܡܦܸܪܲܛܘܼܪܵܐ ܫܹܪܫܵܝܬ݂ܵܐ ܕܛܲܟ݂ܣܵܐ ܘܐܝܼܬ ܠܵܗ̇ ܓܲܒ݂ܵܐ ܕܐܢܪܓܝܐ.

ܬܲܫܥܝܼܬ݂ܵܐ

ܒܹܝܛܵܐ ܬܪܡܘܕܝܢܡܝܩܝܬܐ ܐܲܒ݂ܗ݇ܘܿܢܵܐܝܼܬ ܡܘܼܕܥܠܵܗ̇ ܒ-1971 (ܐܲܝܟ݂ Kältefunktion "ܦܘܼܠܚܵܢܵܐ ܕܩܪܝܪܘܬܐ") ܒܝܲܕ ܐܝܼܢܓܘܿ ܡܘܼܠܹܪ، ܚܲܕ ܡ̣ܢ ܕܵܓ݂ܘܿܠܹ̈ܐ ܕܡܲܕܪܲܫܬܵܐ ܕܦܘܼܪܢܵܣܵܐ ܕܬܪܡܘܕܝܢܡܝܩܐ ܡܠܝܼܠܬ݂ܵܢܵܝܬ݂ܵܐ، ܥܲܠ ܒ݁ܣܝܼܣ ܩܲܕܡܵܝܹ̈ܐ ܩܕ̈ܡܝܐ ܥܲܠ ܦܘܼܠܚܵܢܵܐ ܕ"ܛܶܡܦܸܪܲܛܘܼܪܵܐ ܗܦܝܼܟ݂ܬܵܐ".ܩܠܒܐ:Primary source inline

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