To calculate the porosity of the soil sample, we need to understand what porosity is. Porosity is defined as the ratio of the volume of voids (spaces) in a material to the total volume of the material. In the context of soil, it represents the amount of space available for air and water within the soil structure.
Step-by-Step Calculation of Porosity
- Identify the Relevant Volumes:
- Volume of dry soil (V_dry) = 52 cm³
- Volume of water (V_water) = 48 cm³
-
Volume of soil and water (V_total) = 78 cm³
-
Calculate the Volume of Voids:
The volume of voids (V_voids) can be calculated by subtracting the volume of dry soil from the total volume of soil and water:
[
V_{voids} = V_{total} - V_{dry}
]
Substituting the values:
[
V_{voids} = 78 \, \text{cm}^3 - 52 \, \text{cm}^3 = 26 \, \text{cm}^3
]
-
Calculate the Total Volume of the Soil Sample:
The total volume of the soil sample is the volume of dry soil plus the volume of voids (which includes both water and air):
[
V_{total_soil} = V_{dry} + V_{voids}
]
However, since we already have the total volume (78 cm³), we can use that directly.
-
Calculate Porosity:
Porosity (P) is calculated using the formula:
[
P = \left( \frac{V_{voids}}{V_{total}} \right) \times 100
]
Substituting the values we have:
[
P = \left( \frac{26 \, \text{cm}^3}{78 \, \text{cm}^3} \right) \times 100
]
[
P = \left( \frac{26}{78} \right) \times 100 = \left( \frac{1}{3} \right) \times 100 \approx 33.33\%
]
Correct Answer
The calculated porosity is approximately 33.33%, which does not match any of the provided options. Therefore, it seems there may have been an error in the options or the interpretation of the question.
Explanation of Options
- Option A (28.21%): This value is lower than the calculated porosity and does not represent the ratio of voids to total volume accurately.
- Option B (42.31%): This value is also incorrect based on our calculations. It does not match the calculated porosity.
- Option C (45.83%): This value is higher than the calculated porosity and does not represent the voids accurately.
- Option D (61.54%): This value is significantly higher than the calculated porosity and does not represent the voids accurately.
Common Pitfalls
- Misunderstanding Total Volume: Ensure you are clear on what constitutes the total volume. It includes both the solid and void spaces.
- Confusing Volume of Water with Volume of Voids: Remember that the volume of voids includes both water and air, not just the water volume.
- Calculation Errors: Double-check arithmetic operations, especially when converting fractions to percentages.
Revision Summary
- Porosity is the ratio of void volume to total volume, expressed as a percentage.
- Calculate void volume by subtracting the volume of dry soil from the total volume.
- Use the formula ( P = \left( \frac{V_{voids}}{V_{total}} \right) \times 100 ) to find porosity.
- Be cautious of misinterpretations of volume measurements and ensure calculations are accurate.