Correct Answer - Option 2 : 1.5 × 10

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__Concept:__

In thermodynamics and Fluid Engineering, compressibility is a measure of the relative volume change of a fluid as a response to pressure (or mean stress) change.

Compressibility in Fluid Engineering is expressed as follows:

\(β=\frac{1}{K} = \frac{{ - 1}}{{\frac{{VdP}}{{dV}}}} = -\frac{{dV}}{{VdP}}\)

where, ∂p = change of pressure, ∂v = change in the volume

K = bulk modulus

(-ve) sign indicates, there is a decrease in volume due to an increase in pressure.

__Calculation__:

Given:

β = 0.75× 10^{-9} m^{2}/N, V = 0.01 m^{3}, dP = 2× 10^{7} Pa

Compressibility (β) = \(\frac{1}{k} = \frac{{ - 1}}{{\frac{{VdP}}{{dV}}}} = \frac{{ - dV}}{{VdP}}\)

\(\left( β \right) = \frac{{ - dV}}{{VdP}}\)

\(0.75 × {10^{ - 9}} = - \frac{{ - dV}}{{0.01 × \left( { - 2 × {{10}^7}} \right)}}\)

dV = 1.5 × 10

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