You are curious about the surface area of soil particles near the soil surface.
ID: 237091 • Letter: Y
Question
You are curious about the surface area of soil particles near the soil surface. Suppose that the soil is at a bulk density of 1.38 g cm-3 and contains (by weight) 20% clay, 40% silt, and 40% sand. To make your estimate, you assume some idealized shapes and set some reasonable dimensions: sand particles: spheres of radius=0.50 mm silt particles: spheres of radius=0.01 mm clay particles: discs (thin right circular cylinders) of radius=8 x 10-4 mm and thickness=3 x 10-6 mm. You may assume all particles have a density of 2.65 g cm-3. Estimate the surface area in a thin (3 mm) layer of soil per m2 of land surface.
Explanation / Answer
since density of all the particles is same,
their mass share can also be ,taken as their volume share.
Volume of given land = 0.003*1*1 = 0.003 m^3
volume of clay = 0.20*0.0030*1.38/2.65 = 0.00031245m^3
number of clay particles = 0.00031245/[pi*(8e-7)^2*3e-9] = 5.18e16
volume of silt= 0.40*0.0030*1.38/2.65 = 0.0006249m^3
number of silt particles = 0.0006249/[4/3*pi*(1e-5)^3] = 1.492e11
volume of sand= 0.40*0.0030*1.38/2.65 = 0.0006249m^3
number of sand particles = 0.0006249/[4/3*pi*(5e-4)^3] = 1193471
total surface area = surface are of all particles of all type
= 5.18e16*[2 pi*8e-7*(8e-7+3e-9)] +1.492e11*4*pi*(1e-5)^2 + 1193471*4*pi*(5e-4)^2
= 209081+ 187.5 + 3.75
=209272.25m^2 per m^2 of land
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