Which one of the following quantities is dimensionless?
Specific weight
Specific heat
Specific density
Specific gravity
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UPSC Geoscientist – 2023
Specific weight is weight per unit volume (Force/Volume), with units like N/m³ or lb/ft³. It has dimensions [M L⁻² T⁻²].
Specific heat (or specific heat capacity) is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree. It has units like J/(kg·K) or cal/(g·°C), and dimensions [L² T⁻² θ⁻¹].
Specific density is often used interchangeably with relative density or specific gravity, which is the ratio of the density of a substance to the density of a reference substance (like water). In this context, it is dimensionless. However, sometimes ‘specific density’ might be used ambiguously.
Specific gravity is precisely defined as the ratio of the density of a substance to the density of a reference substance. As it is a ratio of two quantities with the same dimensions (density), it is dimensionless.
Given the options, Specific Gravity (D) is unambiguously a dimensionless quantity. Specific density (C) would also be dimensionless if it means relative density, but specific gravity is the more commonly used term for this dimensionless ratio. If specific density were interpreted as density per unit mass (1/volume), it would be dimensional. Therefore, Specific Gravity is the correct answer.