Question

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

Answer 1

Volume of water, V = 1 L
It is given that water is to be compressed by 0.10%.
∴ Fractional change, ∆V / V = 0.1 / (100 × 1) = 10-3
Bulk modulus, B = ρ / (∆V/V)
ρ = B × (∆V/V)
Bulk modulus of water, B = 2.2 × 109 Nm-2
ρ = 2.2 × 109 × 10-3 = 2.2 × 106 Nm-2
Therefore, the pressure on water should be 2.2 ×106 Nm–2.

Answer 2

original volume of water , V = 1 L
Let change in volume of water is ∆V

A/C to question,
% change in volume of water = ∆V/V × 100
0.1 = ∆V/V × 100
∆V = 0.001

from data, bulk modulus of water,$\beta$ = 2.2 × 10^9 N/m²

use formula, $\beta=\frac{P}{\frac{\Delta{V}}{V}}$
so, P = $\beta\left(\frac{\Delta{V}}{V}\right)$
P = 2.2 × 10^9 × 0.001
P = 2.2 × 10^6 N/m²

hence, the pressure on water should be 2.2 × 10^6 N/m²