Question

If the compressibility of water is \[\sigma \](sigma) per unit atmospheric pressure then the decrease in volume V due to atmospheric pressure p will be:
A) \[\dfrac{{\sigma V}}{p}\]
B) \[\sigma pV\]
C) \[\dfrac{\sigma }{{pV}}\]
D) \[\dfrac{{\sigma p}}{V}\]

Answer 1

Hint: Compressibility is a part of study of thermodynamics. It is a measure of the relative change of a fluid or a solid as a response to a pressure change. It is the fractional change in volume per unit increase in pressure. For each atmospheric increase in pressure, the volume of water would decrease by 46.4 parts per million.

Complete step by step answer:
Step I:
Since water is a liquid and the particles in a liquid are loosely packed. They have distance between them and they can move freely. Water and other liquids are incompressible in normal conditions. Water can be compressed under extreme conditions. It is because density changes due to pressure and temperature is small.
Step II:
Compressibility is given by:
$\dfrac{\dfrac{\Delta V}{V}}{P}=\sigma$
$V$ is the volume and $P$ is the pressure.
\[\dfrac{{\Delta V}}{{pV}} = \sigma \]
\[\Delta V = \sigma pV\]

$\therefore$ The decrease in volume V of water due to atmospheric pressure p will be \[\sigma pV\]. Hence, Option B is the right answer.

Note:
The size of the oxygen atom in water is very rough and they are not spherical in shape. The space between them is ten times their size. Initially, the atoms are apart but they come closer when compressed. But since they are like in nature so they repel each other and that is why it becomes difficult to push the atoms closer.
But when put in extreme conditions, these intermolecular spaces between the molecules decrease and they come closer. They then take a definite shape. That is why water is when compressed or frozen it takes the form of ice which is a solid.