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

Answer:

The volume is reduced by 3.6 milliliters.

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 $\epsilon = -3.0 \times 10^{-4}$ for a volume $V = 12 \,L$ of oil, so we get:

$\Delta V = - 12 \, L \times (-3.0 \times 10^{-4})$

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.