Question

The compressibility of water $4 \times {10^{ - 5}}$per unit atmospheric pressure. What will be the decrease in volume of $100$ cubic centimeter of water under the pressure of $100$ atmosphere?

Answer 1

In order to solve this question, we are going to firstly consider all the values as given in the question, then, the formula for the compressibility of a liquid is taken containing the change in pressure and volume terms, then, putting the values in the equation, the decrease in the volume is found.

Formula used: The compressibility of water is given by the formula
$C = \dfrac{{\Delta V}}{V} \cdot \Delta P$
Where, $\Delta V$is the change in the volume,$V$is the total volume of water and$\Delta P$is the change in the pressure.

Complete step-by-step solution:
In the above question, we can see that
The compressibility of water is given equal to
$C = 4 \times {10^{ - 5}}$per unit atmospheric pressure,
The total volume of the water is given equal to:
$V = 100CC$
The pressure of the water is given as:
$P = 100atm$
Now, the compressibility of water is given by the formula
$C = \dfrac{{\Delta V}}{V} \cdot \Delta P$
Putting the values as given in the question in above equation,

$$4 \times {10^{ - 5}} = \dfrac{{\Delta V}}{{100}} \times 100 \\\ \Rightarrow \Delta V = 4 \times {10^{ - 5}} \\\$$

Hence, the volume of the water has decreased by$4 \times {10^{ - 5}}$ cubic centimeter of water.

Note: In thermodynamics and fluid mechanics, the compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure change. Hence, knowing the pressure change in a system and the total volume of the system, the change in the volume can be found and the compressibility here is referring to the decrease in the volume of water.