For how long should a similar egg for same consumer to be boiled when taken from refrigerator at 5 C? Take the following properties foe egg: k= 10 W/mk, ρ=1200 Kg⁄$m^3$ ,$C_p$=2 Kj/KgK and h=100W/$m^2$ K use lump theory.

An egg as sphere

D=4cm=0.04m

$T_i$=20℃ $t_1$=4 min=240 s

$T_i$=5℃ ,k=10w/mk,h=100w/($m^2$ k),C=2000j/kgk,ρ=1200Kg/$m^3$

The temperature distribution, using lumped system analysis

$\frac{(T-T_∞)}{(T_i-T_∞ )}=exp\frac{⁡-ht}{ρlc}$

Where l= characteristic length which is$\frac{D}{6}$for sphere.

Temperature of consumers taste

$\frac{(T-100)}{(20-100)}=exp\frac{(-100×240×6)}{(1200×0.04×2000)}$

T=0.223(-80)+100=82.15℃

When egg is taken out from refrigerator at

$T_i$=5℃ and T=82.15℃

$\frac{(82.15-100)}{(5-100)}=exp\frac{-(100×t×6)}{(1200×0.04×2000)}$

t=267.5sec=4.45mins