ALTA ALTA Standard Folio Data Arrhenius-Lognormal

Standard Folio Data Arrhenius-Lognormal

ALTA

The Arrhenius-lognormal model [math]\displaystyle{ pdf }[/math] can be obtained first by setting [math]\displaystyle{ \breve{T}=L(V) }[/math] in Eqn. (arrhenius). Therefore: [math]\displaystyle{ \breve{T}=L(V)=C{{e}^{\tfrac{B}{V}}} }[/math] or: [math]\displaystyle{ {{e}^{{{\overline{T}}^{\prime }}}}=C{{e}^{\tfrac{B}{V}}} }[/math] Thus: [math]\displaystyle{ {{\overline{T}}^{\prime }}=\ln (C)+\frac{B}{V} }[/math] Substituting Eqn. (arrh-logn-mean) into Eqn. (arrh-logn-pdf) yields the Arrhenius-lognormal model [math]\displaystyle{ pdf }[/math] or: [math]\displaystyle{ f(T,V)=\frac{1}{T\text{ }{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{{T}'-\ln (C)-\tfrac{B}{V}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}} }[/math]

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