Question 257: Properties of Matter

Question

A certain pressure '$$\mathrm{P}$$' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to $$0.01 \%$$ whereas the liquid gets compressed to $$0.03 \%$$. The ratio of Bulk modulus of water to that of the liquid is $$\frac{3}{x}$$. The value of $$x$$ is ____________.

Accepted Answer

Given, Volume of water, $V_1=1$ litre
Volume of liquid, $V_2=2$ litre,
Pressure $=P$
$$
\begin{aligned}
& \left(\frac{\Delta V}{V} 	imes 100ight)_	ext { water }=0.01 \% ;\\
& \left(\frac{\Delta V}{V} 	imes 100ight)_	ext { liquid }=0.03 \% \\
& 	ext { Bulk modulus, } B=\frac{-P V}{\Delta V} ; \\
& \frac{B_{	ext {water }}}{B_{	ext {liquid }}}=\frac{\left(\frac{\Delta V}{V}ight)_	ext { liquid }}{\left(\frac{\Delta V}{V}ight)_	ext { water }}=\frac{\frac{0.03}{100}}{\frac{0.01}{100}}=3
\end{aligned}
$$
On comparing the given value with $\frac{3}{x}$, we get $x=1$.

Properties of Matter

A certain pressure '$\mathrm{P}' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to 0.01 \% whereas the liquid gets compressed to 0.03 \%. The ratio of Bulk modulus of water to that of the liquid is \frac{3}{x}. The value of x$ is ____________.

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