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

Hint: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.