In Plank's equation for food freezing time $t_f = \frac{\rho_f \lambda}{\Delta T} \left[ \frac{P a}{h} + \frac{R a^2}{k_f} \right]$, the shape factors $(P, R)$ for a sphere of diameter $a$ are:
Options:
(A) $P = 1/6, \; R = 1/24$
(B) $P = 1/2, \; R = 1/8$
(C) $P = 1/4, \; R = 1/16$
(D) $P = 1, \; R = 1/4$
Answer Key:
A
Step-by-Step Solution & Explanation
Plank's geometric coefficients:
- Infinite slab of thickness $a$: $P = 1/2, R = 1/8$
- Infinite cylinder of diameter $a$: $P = 1/4, R = 1/16$
- Sphere of diameter $a$: $P = 1/6, R = 1/24$.