CHE-46

Prater temperature

Internal catalyst ΔT.

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GoverningPrater temperature

Governing equation

\Delta T_{max}=(-\Delta H)C_s \mathcal{D}_e/\lambda

$Cs \in \left[1, 200\right]$

where

dH: dH (kJ/mol)
Cs: Cs (mol/m³)
De: De (m²/s)
lam: lam (W/(m·K))
dT: Prater temperature (K)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\Delta T_{max}=(-\Delta H)C_s \mathcal{D}_e/\lambda

$Cs \in \left[1, 200\right]$

$Cs = 1$ $dT = 0.02$

Along the curve

②

Domain of the variable — blue

Cs_{\min} = 1,\quad Cs_{\max} = 200

$Cs \in \left[1, 200\right]$

$Cs = 1$ $Cs = 1$

Along the curve

③

Response curve — green

\Delta T_{max}=(-\Delta H)C_s \mathcal{D}_e/\lambda

$Cs \in \left[1, 200\right]$

$Cs = 1$ $dT = 0.02$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}dT}{\mathrm{d}Cs}

$Cs \in \left[1, 200\right]$

$Cs = 2.252$ $dT^{\prime} = 0.02$

Along the curve

Lecture brief

Historical brief

From CSTR/PFR mole balances and Arrhenius rates to McCabe–Thiele stages and NTU exchangers, chemical engineering is conservation plus equilibrium. The lab is that design arithmetic. This sheet (CHE-46 — Prater temperature) is the form associated with Prater temperature. Working symbols: $dH$ , $Cs$ , $De$ , $lam$ $\rightarrow$ $dT$ . Internal catalyst ΔT. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

dT

from

dH

Cs

De

lam

in Chemical engineering via

\Delta T_{max}=(-\Delta H)C_s \mathcal{D}_e/\lambda

Internal catalyst ΔT. Use it when a real chemical engineering question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

dH = 80.000\,\mathrm{kJ/mol}

Cs = 20.000\,\mathrm{mol/m^{3}}

De = 1.000e-7\,\mathrm{m^{2}/s}

lam = 0.400\,\mathrm{W/(m·K)}

, the governing relation

\Delta T_{max}=(-\Delta H)C_s \mathcal{D}_e/\lambda

yields

dT = 0.400\,\mathrm{K}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

dH dH80 kJ/molCs Cs20 mol/m³De De1e-7 m²/slam lam0.4 W/(m·K)

Outputs

Prater temperature dT0.400 K

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Internal catalyst ΔT. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube