Specific volume is defined as the volume occupied by a unit mass of a material. It is the reciprocal of density and is an important property in thermodynamics, particularly for gases and fluids.

Symbol and Units

• Cubic meter per kilogram (m³/kg): The base SI unit of specific volume.
• Cubic centimeter per gram (cm³/g): 1 cm³/g = 0.001 m³/kg.
• Liter per kilogram (L/kg): 1 L/kg = 0.001 m³/kg.
• Cubic foot per pound (ft³/lb): 1 ft³/lb ≈ 0.062428 m³/kg.
• Gallon per pound (gal/lb): 1 gal/lb ≈ 0.008345 m³/kg.

Formula

Specific Volume (ν): \( \nu = \frac{V}{m} \), where \( V \) is the volume and \( m \) is the mass.

Key Points

• Specific volume is the reciprocal of density: \( \nu = 1 / \rho \).
• It is an extensive property, meaning it depends on the amount of substance present.
• Specific volume is temperature and pressure dependent, especially for gases.

Applications

• Thermodynamics: Used in calculations involving the properties of gases and fluids.
• Engineering: Design and analysis of systems involving fluid flow and air conditioning.
• Materials Science: Understanding the behavior of materials under different conditions.
• Agriculture: Analyzing soil properties and crop yields.

Material Variance

• Gases: Have high specific volumes due to low density.
• Liquids: Have lower specific volumes compared to gases but higher than solids.
• Solids: Have the lowest specific volumes due to high density.

Examples

Example 1: Convert 0.5 m³/kg to cm³/g:

0.5 m³/kg = 0.5 × 1000 cm³/g = 500 cm³/g.

Example 2: Convert 1.2 L/kg to m³/kg:

1.2 L/kg = 1.2 × 0.001 m³/kg = 0.0012 m³/kg.

Example 3: Convert 2 ft³/lb to m³/kg:

2 ft³/lb ≈ 2 × 0.062428 m³/kg ≈ 0.124856 m³/kg.

Example 4: Convert 3 gal/lb to m³/kg:

3 gal/lb ≈ 3 × 0.008345 m³/kg ≈ 0.025035 m³/kg.

Example 5: Calculate the specific volume if the density of a substance is 800 kg/m³:

Specific volume, \( \nu = 1 / \rho = 1 / 800 = 0.00125 \) m³/kg.