Subtopic: Preservation of food by cooling and freezing
Question Statement:
In Plank's classical freezing time equation $t_f = \frac{\rho \lambda}{\Delta T} \left( \frac{P a}{h} + \frac{R a^2}{k} \right)$, which of the following pairs of geometric factors $(P, R)$ are CORRECT for standard food shapes of minimum dimension $a$?
Options:
(A) Infinite Flat Slab of thickness $a$: $P = 1/2, R = 1/8$
(B) Infinite Long Cylinder of diameter $a$: $P = 1/4, R = 1/16$
(C) Sphere of diameter $a$: $P = 1/6, R = 1/24$
(D) Cube of side $a$: $P = 1/2, R = 1/2$
(E) Infinite Cylinder: $P = 1/4, R = 1/8$
Answer Key:
A, B, C
Step-by-Step Solution & Explanation
For standard Plank geometries with thickness/diameter $a$: Infinite slab has $P = 1/2, R = 1/8$; Infinite cylinder has $P = 1/4, R = 1/16$; Sphere has $P = 1/6, R = 1/24$. (Note: when radius $r$ is used instead, coefficients adjust accordingly).