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Compression

When the volume of a body decreases due to a constant force acting on all of its surfaces, the process is called compression. Analogous to Hooke’s law for elongation, the change in volume $V$ under compression is given by:

$$
\Delta V = - \frac{1}{K} \frac{F}{A} V
$$

The negative sign reflects the reduction in volume. The constant $K$ is called the bulk modulus, analogous to Young's modulus in the case of elongation.

The ratio of force to area,

$$
p = \frac{F}{A}
$$

is known as pressure, and it describes the force acting per unit area. Instead of using the units newtons per square meter (N/m²), the unit pascal (Pa) is commonly used. In the context of air pressure, the unit bar is also frequently used for convenience, with the conversion:

$$
1\,\text{bar} = 1 \cdot 10^5\,\text{Pa}
$$

The average air pressure at sea level is slightly more than 1 bar.

Replacing the reciprocal $1/K$ with the compressibility $\kappa$, we obtain:

$$
\frac{\Delta V}{V} = -\kappa p
$$

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