Air Pollution MCQ with answer and solution

Concept

Aerodynamic diameter and particle density

Formula

d_a = d_g × √(ρ_p / ρ₀)

Step-by-step solution

1. Aerodynamic diameter (da) is the diameter of an equivalent unit-density sphere (ρ₀ = 1 g/cm3) having the same terminal settling velocity as the actual particle. 2. The relationship is governed by da = dg × √(ρ_p / ρ₀), where dg is geometric diameter and ρ_p is particle density. 3. Given ρ_p > 1 g/cm3, the density ratio term √(ρ_p / ρ₀) is greater than 1. 4. Consequently, da is larger than dg. Answer: C

Explanation

The aerodynamic diameter of a particle is defined as the diameter of a standard unit-density sphere (density 1 g/cm3) that exhibits the exact same terminal settling velocity in air. When a particle has a physical density significantly greater than 1 g/cm3, a larger unit-density sphere is required to match its higher settling rate, meaning the aerodynamic diameter exceeds its geometric diameter.

Why the other options are wrong

A) da is smaller than dg only when physical particle density is less than 1 g/cm3 (such as porous soot or hollow cenospheres). B) da equals dg only for spherical particles with a density exactly equal to 1 g/cm3. D) Aerodynamic diameter is fundamentally dependent on particle density and shape factor.

Shortcut

Density > 1 -> Aerodynamic diameter > Geometric diameter (heavy particles settle faster, behaving like larger unit-density spheres).

Common mistake

Inverting the ratio and assuming higher density compacts the aerodynamic diameter.