Question

Determine the change in volume of $6\text{litres}$ of alcohol if the pressure is decreased from $200\text{cm}$ of $Hg$ to $75\text{cm}$ of $Hg$.
[Velocity of sound in alcohol is $1280\text{m/s}$ density of alcohol $=0.81\text{gm/cc}$, density of $Hg=13.6\text{gm/cc}$ and $g=981{\text{cm/s}}^2$]

• A. $0.5\text{mL}$
• B. $0.75\text{mL}$
• C. $1\text{mL}$
• D. $2\text{mL}$

Answer 1

The correct option is B $0.75\text{mL}$

For propagation of sound in liquid $v=\sqrt{\left(B/\rho \right)}$ i.e. $B=v^2\rho$
where $B$ is bulk modulus of liquid, $v$ is the velocity of sound, and $\rho$ is the density of the liquid, here alchohol.
By definition $B=-V\frac{\Delta P}{\Delta V}$
So $-V\frac{\Delta P}{\Delta V}=v^2{\rho }_{al}$
i.e. $\Delta V=\frac{V(-\Delta P)}{{\rho }_{al}{v}^2}$
Here, $\Delta P=H_2{\rho }_{Hg}g-H_1{\rho }_{Hg}g=(75-200)\times 13.6\times 981=-1.667\times {10}^6{\text{dynes/cm}}^2$
So, $\Delta V=\frac{(6\times {10}^3)(1.667\times {10}^6)}{0.81\times (1.280\times {10}^5{)}^2}=0.75\text{cc}=0.75\text{mL}$