Specific gravity versus density (SI units): “The density of a liquid in kg/m^3 is numerically equal to its specific gravity.” State whether this is correct.

Introduction / Context:Specific gravity (SG) is a dimensionless ratio comparing a substance’s density to a reference density, typically water at about 4°C in many engineering contexts. Confusion frequently arises when switching between cgs units (g/cm^3) and SI units (kg/m^3). This question clarifies that numerical equality does not hold in SI unless a conversion is applied.

Given Data / Assumptions:

• Density ρ expressed in SI units kg/m^3.
• Reference density of water ρ_w ≈ 1000 kg/m^3 (near room temperature).
• SG defined as SG = ρ / ρ_w.

Concept / Approach:Because SG is ρ normalized by 1000 kg/m^3, the numerical relation in SI is ρ (kg/m^3) = SG * 1000. Therefore, ρ and SG are not numerically equal unless ρ is expressed in g/cm^3 (where water’s density is approximately 1 g/cm^3). In cgs units, numerical equality happens because ρ_w ≈ 1 g/cm^3, so SG equals ρ in g/cm^3; this does not carry over to SI without multiplying by 1000.

Step-by-Step Solution:

Verification / Alternative check:Example: A light oil with SG = 0.8 has density ρ = 0.8 * 1000 = 800 kg/m^3 in SI, clearly not equal to 0.8 numerically when using kg/m^3. In cgs, ρ = 0.8 g/cm^3 matches SG numerically because the reference is 1 g/cm^3.

Why Other Options Are Wrong:

• True: Incorrect in SI kg/m^3.
• True only when density is in g/cm^3: While numerically true in cgs, the prompt explicitly states kg/m^3, so still false.
• True only at 4°C: Temperature affects ρ_w slightly, but the factor of 1000 in SI remains; equality still does not hold numerically.

Common Pitfalls:Dropping units and comparing bare numbers; mixing SG with specific weight or relative density for gases (which may use air as reference).

Final Answer:False