Question

The dimensional formula \[ [ML^2T^{-2}K^{-1}] \] corresponds to which physical quantity?

• A. Boltzmann constant
• B. Specific heat capacity
• C. Thermal expansion coefficient
• D. Latent heat

Hint:

To identify a physical quantity from its dimensional formula, check which combination of fundamental dimensions (M, L, T, K, etc.) matches the characteristic relation of the quantity, such as energy per temperature for Boltzmann constant.

Answer 1

The Correct Option is A

A neat way to attack this one is to work from the defining relation instead of testing each option by memory. In kinetic theory, the average kinetic energy of a gas molecule is tied to temperature through the Boltzmann constant: $E = k_B T$ (or more precisely $\frac{3}{2}k_BT$ for translational energy, but the constant of proportionality is what we care about here).

Rearranging, $k_B = \dfrac{E}{T}$. Energy carries the dimension $[ML^2T^{-2}]$, and temperature carries $[K]$, so dividing gives $[ML^2T^{-2}K^{-1}]$, exactly the formula given in the question.

Now check that the other three cannot fit this pattern. Specific heat capacity is energy per unit mass per unit temperature, so a mass dimension gets divided out rather than multiplied in. Thermal expansion coefficient is purely $[K^{-1}]$, with no mass or length involved at all. Latent heat is energy per unit mass, so it carries no temperature term whatsoever. None of these can reproduce the given combination, while the Boltzmann constant does so directly and exactly.

So the correct choice is option (1), Boltzmann constant.