Question

What will be the porosity when a soil has its bulk density and particle density of \(1.50\ Mg/m^3\) and \(2.65\ Mg/m^3\), respectively?

• A. 44.4%
• B. 43.4%
• C. 45.3%
• D. 46.3%

Hint:

Porosity = (1 - bulk density/particle density) x 100.

Answer 1

The Correct Option is B

Step 1: Write down the porosity formula.
Porosity of soil tells us what fraction of the total soil volume is pore space, the gaps between particles that can hold air and water. It is worked out from bulk density (mass of dry soil per unit total volume, pores included) and particle density (mass of the solid particles per unit volume of solids alone, with no pores).
The formula is:
\[ \text{Porosity} (\%) = \left(1 - \frac{\text{Bulk density}}{\text{Particle density}}\right) \times 100 \]

Step 2: Put in the given values.
Bulk density \(D_b = 1.50\ Mg/m^3\)
Particle density \(D_p = 2.65\ Mg/m^3\)
\[ \text{Porosity} = \left(1 - \frac{1.50}{2.65}\right) \times 100 \]

Step 3: Work out the division.
\[ \frac{1.50}{2.65} = 0.566 \]
So the solid fraction of the soil is about 0.566, meaning solids fill about 56.6% of the total volume.

Step 4: Subtract from 1 and convert to percent.
\[ 1 - 0.566 = 0.434 \]
\[ 0.434 \times 100 = 43.4\% \]
This 43.4% is the pore space, the part of the soil volume open to hold air and water.

Step 5: Check the other options.
44.4%, 45.3% and 46.3% would only come out of a careless rounding of 1.50/2.65 or an upside down use of the formula. Carrying the division to three decimal places and then subtracting from 1 gives 43.4%, matching none of the other listed values.

Final Answer:
The porosity of the soil works out to 43.4%.
\[ \boxed{43.4\%} \]