How much should the pressure on a litre of ...

Mechanical Properties of Solids

Question : 16 of 21

Marks: +1, -0

How much should the pressure on a litre of water be changed to compress it by 0.10%.

Solution:

Here,

V=1

litre,

\Delta V=0.10\%

V = \frac{0.10}{100} \times 1 = \frac{1}{1000}

litre

Let

\Delta P

= Change in pressure required for compression of 1 litre of water.

B = bulk modulus of water

= 2.2 \times 109 \, \mathrm{N} \, \mathrm{m}^{-2}

Using the relation,

B = \frac{\Delta P}{ \left( \frac{\Delta V}{V} \right) },

we get

\Delta P = B \frac{\Delta V}{V}

= 2.2 \times 10^{9} \times \frac{ \frac{1}{1000} }{1}

= \frac{2.2 \times 10^{9}}{1000}

= 2.2 \times 10^{6} \, \mathrm{N} \, \mathrm{m}^{-2}

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