Compare the measured and theoretical densities of each material ( aluminium and carbon steel)
The Correct Answer and Explanation is:
Answer:
Aluminum:
- Measured density: ~2.70 g/cm³
- Theoretical density: ~2.70 g/cm³
Carbon Steel:
- Measured density: ~7.85 g/cm³
- Theoretical density: ~7.85 g/cm³
Explanation:
Density is defined as mass per unit volume and is typically expressed in grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). Theoretical density refers to the value calculated based on atomic structure and crystal arrangement, assuming a perfect, defect-free solid. Measured density is obtained through experimental methods like Archimedes’ principle or mass-to-volume ratio calculations.
For aluminum, both the measured and theoretical densities are very close to 2.70 g/cm³. This agreement arises because aluminum is a pure element with a face-centered cubic (FCC) crystal structure that packs atoms efficiently. Since high-purity aluminum can be manufactured with minimal internal voids and impurities, the actual measured values align well with theoretical predictions. Minor variations may occur due to the presence of air pockets or oxidation on the surface, but these effects are generally negligible.
For carbon steel, which is an alloy primarily composed of iron and carbon (and sometimes small amounts of manganese, silicon, or other elements), the density is about 7.85 g/cm³ in both theory and practice. The theoretical density is based on the atomic weight of the components and the body-centered cubic (BCC) or FCC lattice structure of the iron matrix. Because carbon steel is an engineered material, manufacturing processes aim for high compaction and uniformity. However, minor discrepancies may occur due to microscopic defects, residual stresses, or alloying variations, though these are usually small.
In both materials, the close match between measured and theoretical densities indicates high material quality and consistency. Deviations, when present, can signal impurities, porosity, or errors in measurement, and are often useful for quality control in engineering and manufacturing.
