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 m2/N, V = 0.01 m3, dP = 2× 107 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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