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Question: The compressibility of water is \(6 \times 10^{- 10}\text{ }\text{N}^{- 1}\text{ }\text{m}^{- 2}.\) ...

The compressibility of water is 6×10−10 N−1 m−2.6 \times 10^{- 10}\text{ }\text{N}^{- 1}\text{ }\text{m}^{- 2}. If one litre is subjected to a pressure of 4×107 N m−2,4 \times 10^{7}\text{ N }\text{m}^{- 2}, the decrease in its volume is

A

10 cc

B

24 cc

C

15 cc

D

12 cc

Answer

24 cc

Explanation

Solution

: Bulk modulus,

B=−P(ΔV/V)\mathbf{B} = - \frac{P}{(\Delta V/V)}

-ve sign shows that with an increase in pressure a decrease in volume occurs.

Compressibility, k=1B=−ΔVPVk = \frac{1}{B} = - \frac{\Delta V}{PV}

Decrease in volume, ΔV=PVK\Delta V = PVK

=4×107×1×6×10−10= 4 \times 10^{7} \times 1 \times 6 \times 10^{- 10}

=24×10−3litre= 24 \times 10^{- 3}litre

=24×10−3×103cm3=24cc= 24 \times 10^{- 3} \times 10^{3}cm^{3} = 24cc