Question

6. What is the bulk modulus of oxygen if 32.0 g of oxygen occupies 22.4 L and the speed of sound in the oxygen is 317 m/s?

Answer 1

Answer:

$\boxed{\sf Bulk \ modulus \ of \ oxygen \approx 143.5 \ kPa}$

Given:

Mass of oxygen (m) = 32.0 g = 0.032 kg

Volume occupied by oxygen (V) = 22.4 L = 0.0224 m³

Speed of sound in oxygen (v) = 317 m/s

To Find:

Bulk modulus of oxygen

Explanation:

$\sf Density \ of \ oxygen \ (\rho) = \frac{m}{V}$

$\sf \implies Bulk \ modulus \ of \ oxygen \ (B) = v^{2} \rho$

$\sf \implies B = v^{2} \times\frac{m}{V}$

$\sf \implies B = {(317)}^{2} \times \frac{0.032}{0.0224}$

$\sf \implies B = {(317)}^{2} \times 1.428$

$\sf \implies B = 100489 \times 1.428$

$\sf \implies B = 143498.292 \: Pa$

$\sf \implies B \approx 143.5 \: kPa$