Question

A cube with edges exactly 2 cm long is made of material with a bulk modulus of 3.5 x 109 n/m2. when it is subjected to a pressure of 3.0 x 105 pa its volume is:

Answer 1

As we know by the formula of bulk modulus

$B = \frac{\Delta P}{-\Delta V/V}$

now we can rearrange it as

$\Delta V/V = -\frac{\Delta P}{B}$

$V_f - V = -V\frac{\Delta P}{B}$

now the final volume after pressure is applied is given as

$V_f = V(1 - \frac{\Delta P}{B})$

now we know that

$\Delta P = 3 \times 10^5 Pa$

$V = 2^3 cm^3 = 8 cm^3$

$B = 3.5 \times 10^9 N/m^2$

now plug in all data

$V_f = 8(1 - \frac{3 \times 10^5}{3.5 \times 10^9})$

$V_f = 7.999 cm^3$

so volume is above after pressure is applied over it