Explanation:
To calculate the requested values, we can use the following formulas:
i. Bulk Density (\(\rho_b\)):
\[ \rho_b = \frac{\text{oven-dry mass of soil}}{\text{volume of soil}} \]
ii. Gravimetric Moisture Content (GMC):
\[ \text{GMC} = \frac{\text{mass of water}}{\text{oven-dry mass of soil}} \times 100 \]
iii. Porosity (\(\phi\)):
\[ \phi = 1 - \frac{\rho_b}{\text{particle density}} \]
iv. Mass of Soil in the Farmland:
\[ \text{Mass of soil in the farmland} = \rho_b \times \text{volume of farmland} \]
Given data:
- Oven-dry mass of soil = 2.5 kg
- Particle density = 2.65 g/cm³
- Internal diameter of the cylindrical core = 10 cm
- Height of the cylindrical core = 20 cm
- Volume of farmland = \(0.5 \, \text{ha} \times 10,000 \, \text{m}^2/\text{ha} \times 0.2 \, \text{m}\)
Let's calculate each value step by step:
i. Bulk Density (\(\rho_b\)):
\[ \rho_b = \frac{2.5 \, \text{kg}}{\pi \times \left(\frac{10 \, \text{cm}}{2}\right)^2 \times 20 \, \text{cm}} \]
ii. Gravimetric Moisture Content (GMC):
\[ \text{GMC} = \frac{\text{mass of water}}{2.5 \, \text{kg}} \times 100 \]
iii. Porosity (\(\phi\)):
\[ \phi = 1 - \frac{\rho_b}{2.65 \, \text{g/cm}^3} \]
iv. Mass of Soil in the Farmland:
\[ \text{Mass of soil in the farmland} = \rho_b \times \left(0.5 \, \text{ha} \times 10,000 \, \text{m}^2/\text{ha} \times 0.2 \, \text{m}\right) \]
Please note that all calculations should be done using consistent units. Also, remember to convert cm to meters in the calculations.
