Archimedes Specific Gravity Assay
Determines the exact hydrostatic specific gravity of bullion, coins, or jewelry items by measuring buoyant water displacement, enabling non-destructive purity testing.
\[ SG = \frac{W_{dry}}{W_{dry} - W_{submerged}} \cdot \rho_{water}(T) \]
Plain Text Formula:
SG = (W_dry / (W_dry - W_submerged)) * rho_water(T)
📐 Variable Definitions & Parameters
| Symbol | Variable Name | Standard Unit | Physical Definition |
|---|---|---|---|
| \[ SG \] | Specific Gravity | dimensionless | Ratio of alloy density to pure water at temperature T |
| \[ W_{dry} \] | Dry Weight | grams (g) | Air weight measured on a high-precision scale |
| \[ W_{submerged} \] | Submerged Weight | grams (g) | Apparent weight when fully suspended in distilled water |
| \[ \rho_{water}(T) \] | Water Density Correction | g/cm³ | Temperature correction factor (~0.9982 g/cm³ at 20°C) |
💡 Worked Engineering Example
Problem Statement:
A solid gold coin weighs 31.10 g in air and 29.49 g submerged in 20°C water. Find its specific gravity.
Step-by-Step Solution:
- Displaced water weight = 31.10 - 29.49 = 1.61 g
- SG = (31.10 / 1.61) * 0.9982 = 19.28
🎯 Result: Specific gravity is 19.28, perfectly matching 24K pure gold (19.32 g/cm³) within 0.2% measurement tolerance.