Question

A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10-4. The bulk modulus of the oil is 6.0 × 109 N/m2 and is independent of the pressure. By how many milliliters does this pressure reduce the volume of the oil?

Answer 1

The volume is reduced by 3.6 milliliters.

Step-by-step explanation:

In order to find the change of volume, we can use the definition of Volumetric strain which is the negative ratio of the change of volume with respect the original volume.

`\epsilon = -\cfrac{\Delta V}{V}`

The negative sign shows that the volume is decreasing. Solving for the change of volume we get

`\Delta V =-V \epsilon`

Thus we can replace the given information of the volume strain on oil
`\epsilon = -3.0 * 10^(-4)` for a volume
`V = 12 \,L` of oil, so we get:

`\Delta V = - 12 \, L * (-3.0 * 10^(-4))`

That give us

`\Delta V = 0.0036\, L`

We can finally multiply by 1000 milliliters per liter to find the reduction in volume of oil.

`\Delta V = 3.6\, mL`

Thus the volume is reduced by 3.6 milliliters.