Density & The Particle Model

Density

• Density is mass per unit volume (recall this equation):

$$\rho = \frac{m}{V}$$

• $\rho$ density in kilograms per metre cubed, kg/m³; $m$ mass in kg; $V$ volume in metres cubed, m³
• Worked example: a 0.54 kg block measuring 0.10 m × 0.05 m × 0.04 m. $V = 0.10 \times 0.05 \times 0.04 = 2.0 \times 10^{-4}$ m³; $\rho = \dfrac{0.54}{2.0 \times 10^{-4}} = 2700$ kg/m³
• 1 g/cm³ $=$ 1000 kg/m³. Water is 1000 kg/m³
• When an object changes shape or state, its mass is conserved, so a change in volume means a change in density

The particle model

• Density differences come from the arrangement: gas particles are far apart, so there is much less mass in the same volume

Required Practical 5: measuring density

• Regular solid: measure the mass on a balance; measure the dimensions with a ruler, or Vernier callipers or a micrometer for small dimensions; calculate the volume (length × width × height); then $\rho = m / V$
• Irregular solid: measure the mass; find the volume by displacement: fill a displacement (eureka) can to the spout, lower the object in on a thread, and collect the displaced water in a measuring cylinder. Its volume equals the object's volume. Or read the rise in level in a measuring cylinder
• Liquid: put an empty measuring cylinder on the balance and zero it (or record its mass), pour in a measured volume, read the mass, then $\rho = m / V$
• Repeat and take a mean. Convert cm³ to m³ ($\div 10^6$) and g to kg ($\div 1000$) if the answer must be in kg/m³

• Errors: reading the measuring cylinder from the wrong eye level (parallax, a random error); water clinging to the object or the thread; the string's own volume; an unzeroed balance (a zero error, systematic)