Changes in Volume

Here we consider changes in volume caused by a force exerted uniformly over the entire exposed surface of the solid.

Definitions:

• Volume Stress ( $\Delta$P ) is the ratio of the magnitude of the normal force F to the area A .
• Volume Strain is the fractional change in volume, $\Delta$V/V . Here, V is the initial volume and $\Delta$V is the change in the volume.
• Bulk Modulus ( B ) is the ratio of the volume stress to the volume strain:

  $${\frac{{\:\rm volume\ stress}}{{\:\rm volume\ strain}}} {\frac{F/A}{\Delta V/V}} {\frac{\Delta P}{\Delta V/V}}$$ (4)

  The negative sign ensures that the Bulk Modulus is always a positive number: forces pressing on a solid from the outside always cause the volume to decrease (compression), so that the fractional change in volume is negative. B has S.I. units of N/m ².