To obtain specific volume from density, simply take the reciprocal of the density.
Understanding Specific Volume and Density
Specific volume and density are inversely related properties of a substance. Here's a breakdown:
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Density (ρ): Density is the measure of how much mass is packed into a given volume. It's usually expressed in units like kilograms per cubic meter (kg/m³) or grams per cubic centimeter (g/cm³). The formula for density is:
ρ = m / V
Where:
- ρ = Density
- m = Mass
- V = Volume
-
Specific Volume (v): Specific volume, on the other hand, represents the volume occupied by a unit mass of a substance. It's often expressed in units like cubic meters per kilogram (m³/kg) or cubic centimeters per gram (cm³/g). The formula for specific volume is:
v = V / m
Where:
- v = Specific volume
- V = Volume
- m = Mass
The Relationship: Reciprocal
As highlighted in the reference: "r = (1/v) = (m/V)", where r represents density (ρ). This equation shows that density (ρ) is the reciprocal of specific volume (v), and vice-versa. Therefore:
- Specific volume (v) = 1 / Density (ρ)
This means if you know the density of a substance, you can directly calculate its specific volume by dividing 1 by the density value.
Calculating Specific Volume
Here's how to get the specific volume from the density:
- Identify the Density: Determine the density (ρ) of the substance. Make sure you have the density value and the correct units. For example, 1000 kg/m³ for water or 7850 kg/m³ for steel.
- Take the Reciprocal: Divide 1 by the density value you found in the previous step.
v = 1 / ρ - Obtain Specific Volume: The result is the specific volume (v) of the substance, in units that correspond to the density units. If the density was in kg/m³, the specific volume will be in m³/kg. For example, if the density is 1000 kg/m³, the specific volume is 1 / 1000 = 0.001 m³/kg.
Example Table
| Property | Formula | Units |
|---|---|---|
| Density (ρ) | m / V | kg/m³, g/cm³ |
| Specific Volume (v) | V / m or 1 / ρ | m³/kg, cm³/g |
Specific Gravity
It's also important to note that the reference also discusses "Specific Gravity," which is the ratio of the density of a substance to the density of water at the same temperature and pressure. It is not the same as specific volume, though understanding it helps understand density conceptually.
Practical Insights
- Specific volume is a useful property, especially in thermodynamics and fluid mechanics.
- It helps to analyze the behavior of gases and liquids under various conditions.
- For a given mass, a substance with a higher specific volume will occupy a larger volume.
