Question

A certain amount of mercury is compressed fom an initial pressure of 500 mpa to a certain amount of final pressure. the final pressure of mercury required, to reduce a unit volume of mercury by 10% is ? (khg=48.5mpa)​

Answer 1

Given:

A certain amount of mercury is compressed from an initial pressure of 500 M Pa to a certain amount of final pressure. Bulk modulus of mercury is 48.5 M Pa.

To Find:

What is the final pressure of mercury required, to reduce a unit volume of mercury by 10% ?

Solution:

We know the formula of bulk modulus in terms of pressure and volumetric strain:

$\mathbf{Bulk \ modulus(K)= -\dfrac{Change\ in\ pressure}{Volumetric \ strain} }$       ...1)

Meaning of negative sign is that on increase or decrease in pressure there are decrease or increase in volume.

Where:

Bulk Modulus = K = 48.5 M Pa

In given question volume is reduce only when pressure increase, so:

Change in pressure = Final pressure - Initial pressure

Change in pressure = P - 500

$\mathbf{Volumetric\ Strain = \frac{\Delta V}{V}=-0.10}$  (Negative sign for decrease in volume)

On putting respective value in equation 1)

$\mathbf{Bulk \ modulus(K)= -\dfrac{Change\ in\ pressure}{Volumetric \ strain} }$

$\mathbf{48.5= -\dfrac{P-500}{-0.1} }$

$\mathbf{48.5= \dfrac{P-500}{0.1} }$

Final pressure = P = 504.85  M Pa

The final pressure of mercury required, to reduce a unit volume of mercury by 10% is 504.85 M Pa.