Question

Dimensional formula for thermal conductivity is (here $K$ denotes the temperature)

• A. $MLT ^{-3} K$
• B. $MLT ^{-2} K$
• C. $MLT ^{-2} K ^{-2}$
• D. $MLT ^{-3} K ^{-1}$

Answer 1

The Correct Option is D

To determine the dimensional formula for thermal conductivity, we need to understand the definition and units involved in thermal conductivity.

Thermal conductivity (\kappa) is defined as the quantity of heat (Q) transmitted through a material with a surface area (A) and thickness (d) per unit time (t) due to a unit temperature gradient (\Delta T).

The formula for thermal conductivity can be expressed as:

\kappa = \frac{Q \cdot d}{A \cdot t \cdot \Delta T}

Let us now represent the dimensions of each parameter involved:

• Heat (Q) has the same dimensional formula as energy, which is [ML^2T^{-2}].
• Thickness (d) and area (A) are length units, giving dimensions [L] and [L^2] respectively.
• Time (t) has the dimensional formula [T].
• Temperature gradient (\Delta T) involves temperature, represented as [K].

Substituting these into the formula for thermal conductivity, we have:

\kappa = \frac{[ML^2T^{-2}] \cdot [L]}{[L^2] \cdot [T] \cdot [K]}

This simplifies to:

[MLT^{-3}K^{-1}]

Thus, the dimensional formula for thermal conductivity is MLT^{-3}K^{-1}.

Correct Answer: MLT^{-3}K^{-1}