$($b$)$ Food with an initial moisture content of $400\%($dry$-$weight basis$)$ is poured into

$0\mathrm{.}5cm$ layers in a tray placed in a freeze drier operating at $40Pa.$ It is to be dried

to $8\%$ moisture $($dry$-$weight basis$)$ at a maximum surface temperature of $55C.$

Assuming that the pressure at the ice front remains constant at $78Pa,$ calculate

i$)$ The drying time

ii$)$ The drying time if the layer of food is increased to $0\mathrm{.}9cm$ and dried under

similar conditions.

Additional data:

The dried food has a thermal conductivity of $0\mathrm{.}03W{m}^{-1}{K}^{-1},$ a density of $470kg{m}^{-3},$

a permeability of $2\mathrm{.}4{10}^{-8}kg{s}^{-1},$ latent heat of sublimation is $2\mathrm{.}95{10}^{3}kJk{g}^{-1}).$

$P_i=P_s+\frac{k_d}{b{}_s}({}_s-{}_i)$

$P_i=$ Partial pressure of water at the sublimation front

$P_s=$ Partial pressure of water at the surface

$k_d=$ Thermal conductivity of the dry layer

$b=$ Permeability of the dry layer

${}_s=$ Latent heat of sublimation

${}_s=$ Surface temperature

${}_i=$ Temperature at the sublimation front

$t_d=\frac{x^2(M_1-M_2)s}{8k_d({}_s-{}_i)}$

$t_d=$ Drying time $($s$)$

$x=$ thickness of the food $(m)$

$=$ bulk density of the dry food $(kg{m}^{-3})$

$M_1=$ Initial water content $($dry weight basis$)$

$M_2=$ Final water content in the dry layer $($dry weight basis$)$