Subtopic: Preservation of food by cooling and freezing
Question Statement:
In food freezing time calculations using Plank's equation $t_f = \frac{\rho \lambda}{T_f - T_a} \left[ \frac{P \cdot a}{h} + \frac{R \cdot a^2}{k} \right]$, which of the following geometric factor pairs ($P, R$) for characteristic dimension $a$ are CORRECT?
Options:
(A) Infinite slab of thickness $a$: $P = 1/2$ and $R = 1/8$
(B) Infinite cylinder of diameter $a$: $P = 1/4$ and $R = 1/16$
(C) Sphere of diameter $a$: $P = 1/6$ and $R = 1/24$
(D) Cube of side $a$: $P = 1/2$ and $R = 1/4$
Answer Key:
A, B, C
Step-by-Step Solution & Explanation
1. Plank's classic equation for freezing time has exact analytical geometric constants derived from steady-state conduction through the frozen layer:
- Infinite flat plate (slab) of thickness $a$: $P = 1/2, R = 1/8$. (Statement A is True)
- Infinite cylinder of diameter $a$: $P = 1/4, R = 1/16$. (Statement B is True)
- Sphere of diameter $a$: $P = 1/6, R = 1/24$. (Statement C is True)
2. A cube has $P = 0.177$ and $R = 0.0417$, NOT $1/2$ and $1/4$. (Statement D is False)