Specific Volume Calculator

Specific Volume

Specific volume is the volume occupied per unit mass. It is the reciprocal of density and is commonly used in thermodynamics and fluid mechanics.

How to use this calculator

1. Enter the total volume \(V\) and mass \(m\) if you want to use \(v = \frac{V}{m}\).
2. Or enter the density \(\rho\) if you want to use \(v = \frac{1}{\rho}\).
3. Make sure your units are consistent, such as \(\text{m}^3\) and \(\text{kg}\), or \(\text{cm}^3\) and \(\text{g}\).
4. Read the result as volume per mass, for example \(\text{m}^3/\text{kg}\).

The formula explained

Specific volume computes the volume occupied by one unit of mass. If you know density, you can also find it by taking the reciprocal because specific volume and density are inverses.

• v = specific volume, the volume per unit mass
• V = total volume
• m = mass
• \(\rho\) = density

Step by step method

1. Write the formula \(v = \frac{V}{m}\) or \(v = \frac{1}{\rho}\).
2. Substitute the known values with units.
3. Divide to find \(v\).
4. State the answer with the correct unit, such as \(\text{m}^3/\text{kg}\).

Worked example

Problem. A liquid has a volume of \(3.6\,\text{m}^3\) and a mass of \(4.5\,\text{kg}\). Find its specific volume.

1. Use \(v = \frac{V}{m}\).
2. Substitute the values, \(v = \frac{3.6}{4.5}\).
3. Compute the quotient, \(v = 0.8\,\text{m}^3/\text{kg}\).

Tips and common mistakes

• Always check units before dividing, because mixed units can give a wrong result.
• If density is given instead of mass and volume, use \(v = \frac{1}{\rho}\) directly.

Frequently asked questions