Kinematic vs dynamic viscosity equality: A liquid shows 1 cP (centipoise) equal to 1 cSt (centistoke) when its density equals 1 g/cm³. Which common liquid satisfies this approximately at room temperature?

Introduction / Context:Dynamic viscosity (μ) and kinematic viscosity (ν) are related by density: ν = μ / ρ. In cgs units, if μ is in cP and ρ in g/cm³, then ν is in cSt. Thus, when ρ ≈ 1 g/cm³, the numerical values of μ (cP) and ν (cSt) coincide, a handy check for common liquids near room temperature.

Given Data / Assumptions:

• Relation: ν (cSt) = μ (cP) / ρ (g/cm³).
• Looking for a liquid with ρ ≈ 1 g/cm³ at ambient conditions.
• Typical room temperature ≈ 20–25°C.

Concept / Approach:Pure water at ~20°C has density ~0.998 g/cm³ and dynamic viscosity ~1.0 cP, yielding kinematic viscosity ~1.0 cSt (more precisely ≈ 1.002 cSt). Therefore, water satisfies the condition closely, making “1 cP ≈ 1 cSt” a commonly used rule-of-thumb for water at ambient conditions.

Step-by-Step Solution:

Verification / Alternative check:Property tables list at 20°C: μ_water ≈ 1.002 cP, ρ_water ≈ 0.998 g/cm³ ⇒ ν ≈ 1.004 cSt, validating the approximation.

Why Other Options Are Wrong:

• Mercury: density ~13.6 g/cm³, so ν ≪ μ numerically.
• Carbon tetrachloride and glycerol have densities far from 1 g/cm³ and very different viscosities.
• “None of these” is incorrect because water satisfies the condition.

Common Pitfalls:Mixing SI and cgs units or forgetting that equality holds only when density ≈ 1 g/cm³.

Final Answer:Water.