#### Specific volume

###### Equation

The challenge of working with volume in the case of seawater is that it depends on variations in temperature, salinity, and pressure. On the other hand, mass is less affected by these variations, which is why it makes sense to work with what we call specific volume, calculated by dividing the volume $V$ by the mass $M$:

$\displaystyle\frac{V}{M}$

However, $M/V$ represents density, so the specific volume is defined as:

$ \alpha = \displaystyle\frac{1}{ \rho }$ |

ID:(11984, 0)

#### Compressibility, infinitesimal

###### Equation

The compressibility of a gas, denoted by $\kappa$, can be defined as the ratio of the volume change $\Delta V/V$ to the pressure increase $\Delta p$. Mathematically, it is expressed in infinitesimal form as:

$ k_p = -\displaystyle\frac{1}{ V }\displaystyle\left(\displaystyle\frac{\partial V }{\partial p }\displaystyle\right)_ T $ |

The negative sign is associated with the fact that an increasing pressure $dp > 0$ leads to a decrease in volume $dV < 0$.

ID:(210, 0)

#### Ocean water compressibility coefficient

###### Equation

In the case of the ocean, the concept of specific volume $\alpha$ is used instead of the compressibility coefficient $k_p$. Therefore, it is necessary to convert the compressibility coefficient, which is typically defined in terms of volume variation, into terms of specific volume variation. Thus, in response to a pressure variation $p$, the compressibility coefficient in terms of specific volume $\alpha$ can be expressed as:

$ k_p = -\displaystyle\frac{1}{ \alpha }\left(\displaystyle\frac{ \partial\alpha }{ \partial p }\right)_{ T , S }$ |

The compressibility coefficient with $k_p$ is defined by

$ k_p = -\displaystyle\frac{1}{ V }\displaystyle\left(\displaystyle\frac{\partial V }{\partial p }\displaystyle\right)_ T $ |

In the case of oceanic water, we work with the specific volume

$ \alpha = \displaystyle\frac{1}{ \rho }$ |

instead of the volume $V$. Therefore, a change of variable can be performed, resulting in the compressibility coefficient as

$ k_p = -\displaystyle\frac{1}{ \alpha }\left(\displaystyle\frac{ \partial\alpha }{ \partial p }\right)_{ T , S }$ |

ID:(11981, 0)

#### Measured compressibility coefficient for different temperatures

###### Description

The compressibility coefficient for oceanic water, measured as a function of temperature, follows the trend shown in the following graph:

In general, it is observed that compressibility:

- decreases with increasing pressure.

- decreases with increasing temperature.

ID:(11988, 0)

#### Measured compressibility coefficient for different salinities

###### Description

The compressibility coefficient for oceanic water, measured as a function of salinity, exhibits the trend shown in the following graph:

In general, it is observed that compressibility:

- decreases with increasing salinity.

- decreases with increasing temperature.

ID:(11989, 0)