The specific weight of water at ordinary pressure and temperature is 62.4 lb/ft3 (9.81 kN/m3 ). The specific gravity of mercury is 13.55. Calculate the density specific weight and density of mercury
The specific weight of water at ordinary pressure and
temperature is 62.4 lb/ft3 (9.81 kN/m3
). The specific
gravity of mercury is 13.55. Calculate the density
specific weight and density of mercury
The Correct Answer and Explanation is :
To calculate the specific weight and density of mercury based on the given data, we need to use the concept of specific gravity and the specific weight of water.
1. Specific Weight of Mercury
Specific weight ((\gamma)) is the weight per unit volume and is given by the equation:
[
\gamma = \text{Specific Gravity} \times \gamma_{\text{water}}
]
Where:
- (\gamma_{\text{water}}) is the specific weight of water.
- The specific gravity (SG) of mercury is given as 13.55.
- The specific weight of water at ordinary temperature and pressure is 62.4 lb/ft³.
Now, we can calculate the specific weight of mercury:
[
\gamma_{\text{mercury}} = 13.55 \times 62.4 \, \text{lb/ft}^3
]
[
\gamma_{\text{mercury}} = 844.92 \, \text{lb/ft}^3
]
Thus, the specific weight of mercury is approximately 844.92 lb/ft³.
2. Density of Mercury
The density ((\rho)) is defined as the mass per unit volume and is related to the specific weight by the equation:
[
\rho = \frac{\gamma}{g}
]
Where:
- (\gamma) is the specific weight.
- (g) is the acceleration due to gravity, which is 32.174 ft/s² in imperial units.
Substituting the values:
[
\rho_{\text{mercury}} = \frac{844.92 \, \text{lb/ft}^3}{32.174 \, \text{ft/s}^2}
]
[
\rho_{\text{mercury}} \approx 26.23 \, \text{lb/ft}^3
]
Thus, the density of mercury is approximately 26.23 lb/ft³.
3. Density in SI Units
To convert this to SI units (kg/m³), we use the conversion factor 1 lb/ft³ = 16.0185 kg/m³.
[
\rho_{\text{mercury}} = 26.23 \, \text{lb/ft}^3 \times 16.0185 \, \text{kg/m}^3
]
[
\rho_{\text{mercury}} \approx 420.8 \, \text{kg/m}^3
]
Thus, the density of mercury is approximately 420.8 kg/m³.
Summary:
- Specific weight of mercury: 844.92 lb/ft³
- Density of mercury: 26.23 lb/ft³ (or 420.8 kg/m³)
Explanation:
- Specific gravity is the ratio of the density of a substance to the density of water. Mercury’s specific gravity is given as 13.55, meaning it is 13.55 times denser than water.
- The specific weight is the product of the specific gravity and the specific weight of water.
- To calculate the density from the specific weight, we divide the specific weight by the acceleration due to gravity.