True porosity is a fundamental property in geology and materials science that measures the fraction of void space in a material. It represents the ratio of the volume of pores (voids) to the total volume of a material. True porosity is crucial in understanding fluid storage capacity, permeability, and other physical properties of rocks, soils, and porous materials.

The formula for true porosity is:

\[ \phi = \frac{V_p}{V_b} = \frac{V_b - V_g}{V_b} \]

Where:

- \( \phi \) is the true porosity (dimensionless or as a percentage)
- \( V_p \) is the pore volume (in cubic units, e.g., cm³)
- \( V_b \) is the bulk volume of the material (in cubic units, e.g., cm³)
- \( V_g \) is the grain volume (solid material volume) (in cubic units, e.g., cm³)

Let's calculate the true porosity for a rock sample:

- Given:
- Bulk volume (\( V_b \)) = 100 cm³
- Grain volume (\( V_g \)) = 75 cm³

- Apply the true porosity formula: \[ \phi = \frac{V_b - V_g}{V_b} \]
- Substitute the known values: \[ \phi = \frac{100 \text{ cm³} - 75 \text{ cm³}}{100 \text{ cm³}} \]
- Perform the calculation: \[ \phi = \frac{25 \text{ cm³}}{100 \text{ cm³}} = 0.25 \]
- Convert to percentage (optional): \[ \phi = 0.25 \times 100\% = 25\% \]

Let's visualize the concept of true porosity:

This diagram illustrates:

- The bulk volume (\( V_b \)) represented by the entire rectangle
- The grain volume (\( V_g \)) shown as gray circles (solid material)
- The pore space (\( V_p \)) as the white areas between grains
- True porosity (\( \phi \)) is the ratio of pore space to bulk volume

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