Question

The temperature dependence of the diffusivity can generally be described by

• A. Arrhenius equation
• B. Fick’s law
• C. Sorption kinetics
• D. Permeation method

Hint:

The Arrhenius equation ($D = D_0 e^{-E_a/RT}$) is used to model the temperature dependence of many rate-limiting processes in food engineering, including diffusivity, reaction rates, and microbial destruction.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Diffusion is the net movement of molecules from a region of higher concentration to a region of lower concentration, driven by thermal energy.
The rate of diffusion is determined by the diffusion coefficient (diffusivity, $D$).
Since temperature reflects the average kinetic energy of molecules, raising the temperature increases molecular velocity and the rate of diffusion.

Step 2: Detailed Explanation:
The temperature dependence of the diffusion coefficient is modeled using an Arrhenius-type equation:
\[ D = D_0 \cdot \exp\left(-\frac{E_a}{R \cdot T}\right) \]
Where:
$D$ is the diffusivity at temperature $T$ (in K).
$D_0$ is the pre-exponential factor (maximum diffusivity at infinite temperature).
$E_a$ is the activation energy for diffusion (the energy barrier that must be overcome for a molecule to move).
$R$ is the universal gas constant.
$T$ is the absolute temperature (in Kelvin).
This exponential relationship shows that diffusivity increases rapidly with temperature, which is critical for modeling drying, rehydration, and chemical migration in dairy products during storage.
For comparison:
- Fick’s laws (B) describe the rate of diffusion under a concentration gradient but do not model its temperature dependence.
- Sorption kinetics (C) describe the rate of moisture absorption.
- The permeation method (D) is an experimental technique used to measure gas transport through films.
Therefore, the Arrhenius equation is the correct mathematical model.

Step 3: Final Answer
The temperature dependence of diffusivity is described by the Arrhenius equation.