Respuesta :
Explanation:
It is given here that a slab is made up of dry wood.
Thickness of slab = 4 inch
It is given condition that the edges of the slab are sealed and exposed to air.
Given the relative humidity of air = 40%
The surface of slab is unsealed and reached to the equilibrium moisture content = [tex]\frac{8 lb H_{2}O}{100 lb dry wood}[/tex].
Given, the diffusivity of water in the slab = [tex]6 \times 10^{-6} cm^{2}/s[/tex].
As per the given condition 1% moisture content will be taken by multiplying the moisture content by 1%, i.e. 0.01.
It is given that the thickness of slab is in inch, so converting the thickness of slab in cm as follows.
Thickness of slab = [tex]4 inch \times 2.54 inch/cm[/tex]
= 10.16 cm (As, 1 inch = 2.54 cm)
Since, the equilibrium moisture content is required to calculate at the center of the slab.
The center of the slab, from the semi-infinite slab solution will be taken from thickness t = 0.
The thickness at center = 10.16 cm
Hence, calculate total thickness at the center of slab as follows.
[tex]\frac{\text{total thickness of slab}}{2}[/tex]
= 5.08 cm
Now, by semi-infinite solution, and by 40% relative humidity of air, time for moisture content to reach at the center of the slab, to 1% of its equilibrium value will be calculated as follows.
Time(Seconds) = [tex]\frac{thickness^{2}(cm^{2}) \times \text{relative humidity} \times 0.01 \times \text{equilibrium content} \times \text{equilibrium moisture}}{\text{diffusivity(cm/s)}}[/tex]
Time (sec) = [tex]\frac{5.08 cm \times 5.08 cm \times 0.4 \times \text{relative humidity} \times 0.01 \text{equilibrium content} \times 8 lb H_{2}O}{100 lb dry.wood \times 6 \times 10{-6} cm^{2}/s \text{diffusivity}}[/tex]
Time (Seconds) = 1376.34 seconds
Thus, we can conclude that the time required for the moisture content at the center of the slab to reach to 1 % of equilibrium value is 1376.34 seconds.
