The specific gravity of mercury at 20° C is (13.546). Calculate the density of mercury in (lb /ft), and then calculate the volume in ft occupied by 215 kg of mercury.
The Correct Answer and Explanation is :
To calculate the density of mercury in lb/ft³ and the volume occupied by 215 kg of mercury, let’s break the problem into two parts.
Step 1: Find the density of mercury in lb/ft³
The specific gravity (SG) of mercury is 13.546. Specific gravity is the ratio of the density of a substance to the density of water at a specified temperature (usually 4°C, where water’s density is 1 g/cm³).
- Formula for density: Density (in g/cm³)=SG×Density of water (in g/cm³)\text{Density (in g/cm³)} = \text{SG} \times \text{Density of water (in g/cm³)} Since the density of water is 1 g/cm³, the density of mercury in g/cm³ is simply the specific gravity: Density of mercury=13.546 g/cm³\text{Density of mercury} = 13.546 \, \text{g/cm³}
- Convert density to lb/ft³: 1 g/cm³ = 62.43 lb/ft³. To convert the density of mercury from g/cm³ to lb/ft³: Density of mercury (in lb/ft³)=13.546 g/cm³×62.43 lb/ft³=844.45 lb/ft³\text{Density of mercury (in lb/ft³)} = 13.546 \, \text{g/cm³} \times 62.43 \, \text{lb/ft³} = 844.45 \, \text{lb/ft³} So, the density of mercury is approximately 844.45 lb/ft³.
Step 2: Find the volume occupied by 215 kg of mercury
Next, we calculate the volume occupied by 215 kg of mercury. We know the density of mercury in kg/m³ and need to use the following formula for volume:
- Convert mass from kg to lb: 215 kg×2.20462=474.99 lb215 \, \text{kg} \times 2.20462 = 474.99 \, \text{lb}
- Use the formula for volume: Volume=MassDensity\text{Volume} = \frac{\text{Mass}}{\text{Density}} Volume=474.99 lb844.45 lb/ft³=0.562 ft³\text{Volume} = \frac{474.99 \, \text{lb}}{844.45 \, \text{lb/ft³}} = 0.562 \, \text{ft³}
Thus, the volume occupied by 215 kg of mercury is approximately 0.562 ft³.
Final Answer:
- The density of mercury is 844.45 lb/ft³.
- The volume occupied by 215 kg of mercury is approximately 0.562 ft³.