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In fluid mechanics, the specific gravity (relative density) of a substance is defined as the ratio of its density to the density of water at . Using typical sea-level values and , what is the specific gravity of air?
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19. Fluid Mechanics
Density
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You want to verify if a 70-g crown is in fact made of pure gold (19.32 g/cm3 ), so you lower it by a string into a deep bucket of water that is filled to the top. When the crown is completely submerged, you measure that 3.62 mL of water has overflown. Is the crown made of pure gold?
A
Yes
B
No
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Calculate the volume of the crown using the volume of water displaced. Since 1 mL of water is equivalent to 1 cm³, the volume of the crown is 3.62 cm³.
Determine the density of the crown using the formula: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). Here, the mass of the crown is 70 g and the volume is 3.62 cm³.
Substitute the known values into the density formula: \( \text{Density} = \frac{70 \text{ g}}{3.62 \text{ cm}^3} \).
Compare the calculated density of the crown with the known density of pure gold, which is 19.32 g/cm³.
If the calculated density is equal to or very close to 19.32 g/cm³, then the crown is made of pure gold. Otherwise, it is not.
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