Subtopic: Preservation of food by cooling and freezing
Question Statement:
Using Plank's equation for freezing time of a slab of food $t_f = \frac{\rho \lambda}{T_f - T_a} \left[ \frac{P a}{h} + \frac{R a^2}{k} \right]$, what are the geometric shape factors $P$ and $R$ for an infinite slab geometry?
Options:
(A) $P = 1/2, R = 1/8$
(B) $P = 1/4, R = 1/16$
(C) $P = 1/6, R = 1/24$
(D) $P = 1, R = 1/2$
Answer Key:
A
Step-by-Step Solution & Explanation
For an infinite flat slab of thickness $a$, Plank's shape factors are $P = 1/2$ and $R = 1/8$. For an infinite cylinder of diameter $a$, $P = 1/4, R = 1/16$. For a sphere of diameter $a$, $P = 1/6, R = 1/24$.