The Archimedes Experiment
The buoyancy experiment, attributed to Archimedes of Syracuse around 250 BC, is a simple yet elegant method for determining the density of an irregularly shaped object without measuring its volume directly. According to legend, King Hiero II asked Archimedes to determine whether a crown was made of pure gold without damaging it. By weighing the crown in air and then in water, Archimedes could calculate its density and compare it to pure gold.
The method works by measuring the buoyant force, which equals the weight of water displaced. Since the displaced volume equals the object's volume when fully submerged, combining the mass (from weight in air) with volume (from buoyant force) gives the density. This technique is still used today in gemology, metallurgy, and materials science for precise density measurements of solid objects.
Measurement Method
The accuracy depends on precise weight measurements and knowing the exact water density, which varies with temperature. At 4 degrees C, water has maximum density of 1000 kg/m3. At 20 degrees C, it drops to about 998.2 kg/m3.
Material Identification
| Material | Density (kg/m³) | Specific Gravity |
|---|---|---|
| Gold | 19,300 | 19.3 |
| Silver | 10,490 | 10.5 |
| Copper | 8,960 | 8.96 |
| Iron | 7,874 | 7.87 |
| Aluminum | 2,700 | 2.70 |
Frequently Asked Questions
How accurate is this method?
With a precision balance capable of 0.01g resolution, the buoyancy method can determine density to within 0.1-0.5%. Sources of error include air bubbles clinging to the surface, the wire or thread holding the object, water absorption by porous materials, and water temperature uncertainty. For highest accuracy, the object should be clean and degassed, and the support wire should be as thin as possible.
Can this method detect gold plating?
Yes, if the plating is thick enough to affect the average density measurably. A gold-plated tungsten bar (tungsten density 19,250 vs gold 19,300) would be nearly undetectable because the densities are so close. However, gold-plated copper or brass (density around 8,500) would show a significantly lower density than pure gold, easily detectable. This is why density testing alone is not sufficient for high-value gold authentication.
What if the object floats?
If the object floats, a sinker method is used: first weigh a dense sinker in water, then attach the floating object and weigh the combination in water. The difference gives the buoyant force on the floating object alone. This technique is used for measuring the density of wood, foam, and other materials lighter than water. Alternatively, a denser fluid in which the object sinks can be used.