Question

The relationship between the Del factor, temperature and time is given as___________

• A. Δ = 1/(A.t. e‐E/RT)
• B. Δ = A.t. e‐E/RT
• C. Δ = A.t. eE/RT
• D. Δ = A.t.T

Hint:

The Del factor is crucial in designing sterilization cycles (like in a bioreactor or canning) to ensure a safe "log reduction" of pathogens or spoilage organisms.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question relates to thermal processing and sterilization kinetics. The "Del factor" ($\Delta$) is a measure of the cumulative sterilization effect. It is derived from the Arrhenius equation applied to the destruction of microorganisms.
Key Formula or Approach:
The rate of microbial destruction ($k$) follows the Arrhenius equation: $k = A \cdot e^{-E/RT}$.
The Del factor is defined as the natural log of the ratio of initial to final number of organisms: $\Delta = \ln(N_0/N)$.
For a constant temperature process, $\Delta = k \cdot t$.

Step 2: Detailed Explanation:

• Substitution: By substituting the Arrhenius rate constant into the Del factor definition, we get $\Delta = (A \cdot e^{-E/RT}) \cdot t$.

• Variables:
• $A$: Arrhenius frequency factor (pre-exponential factor).

• $t$: Time.

• $E$: Activation energy.

• $R$: Universal gas constant.

• $T$: Absolute temperature in Kelvin.

• Analysis of Options: Option (B) correctly represents this linear multiplication of time with the exponential temperature dependency.

Step 3: Final Answer:
The Del factor is directly proportional to time and exponentially related to the inverse of temperature as per the equation $\Delta = A \cdot t \cdot e^{-E/RT}$. Option (B) is correct.