Question

The thermal conductivity of a substance may be defined as the rate of heat transfer per unit length per unit temperature difference. The primary dimensions of thermal conductivity in the M-L-T-θ are:

A. M²L/T²θ
B. M²L^/Tθ
C. L²/MT²θ
D.ML/T³θ
E. ML²/T³θ

Answer 1

The primary dimensions of thermal conductivity in the M-L-T-θ system are MLT^-3θ^-1, as thermal conductivity is related to the mass, length, time, and temperature units involved in the rate of conductive heat transfer.

Step-by-step explanation:

The thermal conductivity of a substance is defined as the rate of heat transfer per unit length per unit temperature difference, typically measured in watts per meter per kelvin (W/m·K). When assessing the dimensions of thermal conductivity using primary dimensions M (mass), L (length), T (time), and θ (temperature), we find that the correct dimensional formula is MLT-3θ-1. This derives from considering dimensional analysis of the formula for conductive heat transfer, Q/t = kA(Th -Te)/d, where Q/t is the rate of heat transfer, k is the thermal conductivity, A is the surface area, d is the thickness, and (Th -Te) is the temperature difference.

From this relationship, it's deduced that the units of thermal conductivity involve mass (M), length (L), time (T), and temperature (θ). Thus, the primary dimensions of thermal conductivity are given by MLT-3θ-1, which corresponds to option D.