Paraffin displacement (clod method): A soil clod is oven-dry, then coated with paraffin and weighed. Total weight (soil + paraffin) = 460 g. When immersed, it displaces 299 cm^3 of water. Paraffin weighs 10 g and has specific gravity 0.9. If Gs (solids) = 2.5, compute the void ratio e of the soil.

Introduction / Context:The paraffin (clod) method measures the bulk volume of an irregular soil clod by displacement after coating with a thin paraffin film. Knowing the dry mass and particle specific gravity allows determination of the volume of solids and thus the void ratio e = Vv / Vs. This problem exemplifies careful accounting for the paraffin shell volume.

Given Data / Assumptions:

• Total mass (soil + paraffin) = 460 g; paraffin mass = 10 g.
• Displaced water volume (coated clod) = 299 cm^3.
• Specific gravity: paraffin = 0.9; soil solids Gs = 2.5; water density 1 g/cm^3.
• Soil clod is oven-dry (mass of soil solids = 460 − 10 = 450 g).

Concept / Approach:

External volume from displacement includes soil + paraffin. Subtract the paraffin volume to get the bulk soil volume. Then compute Vs from dry mass and Gs. The void volume is Vv = V − Vs, and e = Vv / Vs.

Step-by-Step Solution:

Verification / Alternative check:

Dimensional consistency: volumes in cm^3 and masses in g with water at 1 g/cm^3 yield a dimensionless e. The value e ≈ 0.60 is typical for a medium-dense sandy silt/sand mixture, providing a reasonableness check.

Why Other Options Are Wrong:

0.55, 0.65, 0.70 deviate from the precise computation; 0.48 is too low given the volumes.

Common Pitfalls:

Forgetting to subtract the paraffin volume; using wet mass instead of dry mass for Vs; mixing units; rounding too early.

Final Answer:

0.60