Question

How much should the pressure on a litre of water be changed to compress it by 0.10%? carry one quarter of the load.

Answer 1

 

Given

• Volume of water: \( V = 1 \,\text{L} \) (actual value not needed, only fractional change matters).
• Required compression: \( 0.10\% \) decrease in volume.
• Bulk modulus of water: \( B = 2.2 \times 10^{9} \,\text{N m}^{-2} \).

Step 1: Fractional Change in Volume

Compression of \(0.10\%\) means: \[ \frac{\Delta V}{V} = \frac{0.10}{100} = 0.001 \] (Here \(\Delta V\) is negative for compression, but we are interested in magnitude of pressure change.)

Step 2: Use Bulk Modulus Relation

Bulk modulus: \[ B = \frac{\Delta P}{\left| \dfrac{\Delta V}{V} \right|} \] Therefore, \[ \Delta P = B \left| \frac{\Delta V}{V} \right| = 2.2 \times 10^{9} \times 0.001 = 2.2 \times 10^{6} \,\text{N m}^{-2} \]

Final Answer

The pressure on one litre of water must be changed by \[ \boxed{\Delta P = 2.2 \times 10^{6} \,\text{N m}^{-2}} \] to compress it by \(0.10\%\).