To convert the density of mercury from grams per cubic centimeter (g/cm³) to pounds per cubic inch (lb/in³), we can follow a systematic approach using the given conversions:
- 1 lb = 454 g
- 1 in = 2.54 cm
We know the density of mercury is 13.6 g/cm³. First, we convert grams to pounds:
Density in lb/in³:
Density in lb/in³ = Density in g/cm³ × (1 lb / 454 g) × (1 cm³ / (2.54 in)³)
Calculating the volume conversion:
- (2.54 cm)³ = 2.54 × 2.54 × 2.54 = 16.387 cm³
- Therefore, 1 cm³ = 1 / 16.387 in³
Now, substituting the values into the density conversion formula:
Density in lb/in³ = 13.6 g/cm³ × (1 lb / 454 g) × (1 cm³ / 16.387 in³)
First, let’s convert the grams to pounds:
13.6 g/cm³ / 454 g/lb = 0.02998 lb/cm³.
Now converting cm³ to in³:
0.02998 lb/cm³ × 16.387 cm³/in³ = 0.4908 lb/in³.
Thus, the density of mercury is approximately 0.4908 lb/in³.