Question

The variation of thermal conductivity of a metal with temperature is often correlated using an expression of the form k=knaught+bT where k is the thermal conductivity and T is the temperature (in Kelvin) The units of 'b' in the SI system is

A. W/mK
B. W/m
C. W/mK²
D. None

Answer 1

The units of the constant 'b' in the expression for variation of thermal conductivity with temperature in the SI system are (C) W/mK².

Step-by-step explanation:

The question is asking for the units of the constant 'b' in the correlation expression for the variation of thermal conductivity of a metal with temperature, which is given as k = k_0 + bT.

The unit for the thermal conductivity, k, is in W/mK (watts per meter per kelvin). Considering the temperature, T, in Kelvin (K), when we replace T in the equation, the units of b must ensure that the units of the entire equation remain consistent as W/mK. Therefore, the unit of b must be W/mK² since it is multiplied by T (in Kelvin) to maintain the proper dimensionality of thermal conductivity. Consequently, the option that correctly represents the units of 'b' in the SI system is (C) W/mK².