Question

Bulk modulus of water is $2 \times {10^9}Pa$ .Air is ____ times more compressible than water.
(A) $200$
(B) $2 \times {10^3}$
(C) $2 \times {10^5}$
(D) $2 \times {10^4}$

Answer 1

Hint Here, we know the bulk water module with the pascal unit when we equate air and compressible compared to water. According to the bulk modulus of water and air, we describe the formula, then compare the value of both and also find how many times more than water is air.
Useful formula
The bulk modulus $k > 0$ can be formality defined by the equation
$K = - V\dfrac{{dP}}{{dV}}$
Where,
$P$ is pressure
$V$ is initial volume of substance
$\dfrac{{dP}}{{dV}}$ denotes the derivative pressure with respect to volume.

Complete step by step solution
Given by,
Bulk modulus of water is $2 \times {10^9}Pa$
We find the compressibility of water than air,
A substance 's bulk modulus is known as the ratio of an increase in infinitesimal pressure to a decrease in volume. The bulk modulus is only applicable to a fluid. It is either $K$ or $B$.
According to the Bulk modulus and compressibility,
We can be written as,
\[\dfrac{{{B_{Water}}}}{{{B_{air}}}} = \dfrac{{{C_{air}}}}{{{C_{water}}}}\]
Substituting the given value in above equation,
\[\dfrac{{{B_{Water}}}}{{{B_{air}}}} = \dfrac{{{C_{air}}}}{{{C_{water}}}}\]$ = $\[\dfrac{{2 \times {{10}^9}}}{{1 \times {{10}^5}}}\]
On simplifying,
We get, $2 \times {10^4}$
Hence,
Bulk modulus of water is $2 \times {10^9}Pa$ .Air is $2 \times {10^4}$ times more compressible than water.

Thus, option D is the correct answer.

Note It refers to the uniform compression of any substance, which is most widely used to describe the action of fluids according to the bulk modulus of B. It can be used to predict compression, calculate density, and to indirectly demonstrate the kinds of chemical bonding within a material.