Understanding Specific Gravity and Mercury

The question asks for the specific gravity of mercury. Specific gravity is a dimensionless quantity that represents the ratio of the density of a substance to the density of a reference substance.

Definition of Specific Gravity

Specific gravity is defined as:

\[ \text{Specific Gravity} = \frac{\text{Density of Substance}}{\text{Density of Reference Substance}} \]

For liquids and solids, the reference substance is typically water at a specific temperature and pressure (often \(4^\circ \text{C}\) and 1 atmosphere, where its density is approximately \(1000 \, \text{kg/m}^3\) or \(1.0 \, \text{g/cm}^3\)).

Density Values for Calculation

To calculate the specific gravity of mercury, we need the density of mercury and the density of water:

• Density of Mercury (\( \rho_{\text{mercury}} \)): Approximately \(13600 \, \text{kg/m}^3\) or \(13.6 \, \text{g/cm}^3\) at room temperature.
• Density of Water (\( \rho_{\text{water}} \)): Approximately \(1000 \, \text{kg/m}^3\) or \(1.0 \, \text{g/cm}^3\) at standard conditions.

Calculating Specific Gravity of Mercury

Using the formula and the density values, we can calculate the specific gravity of mercury:

Specific Gravity of Mercury \( = \frac{\text{Density of Mercury}}{\text{Density of Water}} \)

Using \( \text{g/cm}^3 \) units:

\[ \text{Specific Gravity} = \frac{13.6 \, \text{g/cm}^3}{1.0 \, \text{g/cm}^3} = 13.6 \]

Using \( \text{kg/m}^3 \) units:

\[ \text{Specific Gravity} = \frac{13600 \, \text{kg/m}^3}{1000 \, \text{kg/m}^3} = 13.6 \]

The specific gravity of mercury is \(13.6\). It is a dimensionless quantity, meaning it has no units, as it is a ratio of two densities with the same units.

Comparing with Options

Let's compare our calculated value with the given options:

The calculated specific gravity of mercury, \(13.6\), matches Option 3.

Specific Gravity Concepts Revision

Here is a brief revision of key concepts related to specific gravity:

• Specific gravity is also known as relative density.
• It indicates how much denser (or less dense) a substance is compared to the reference substance (usually water).
• If specific gravity is greater than 1, the substance is denser than water and will sink in water.
• If specific gravity is less than 1, the substance is less dense than water and will float on water.
• Specific gravity is often used in various fields like civil engineering, soil mechanics, and fluid mechanics.

Additional Information on Mercury Properties

Mercury is a unique element with interesting properties:

• It is the only metal that is liquid at standard temperature and pressure.
• Its symbol is Hg, and its atomic number is 80.
• Mercury has a very high density compared to most other liquids.
• It has a relatively high surface tension.
• Mercury and its compounds are toxic and should be handled with care.
• Historically, mercury was used in thermometers, barometers, and other scientific instruments due to its properties, including its high specific gravity and consistent expansion with temperature.