Question

What is the dimension of thermal conductivity?

• A. $\left[{\mathrm{MLT}}^{-1}{\mathrm{\theta }}^{-1}\right]$
• B. $\left[{\mathrm{MLT}}^{-3}{\mathrm{\theta }}^{-1}\right]$
• C. $\left[{\mathrm{M}}^2{\mathrm{LT}}^{-3}{\mathrm{\theta }}^{-2}\right]$
• D. $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\mathrm{\theta }\right]$

Answer 1

The correct option is B

$\left[{\mathrm{MLT}}^{-3}{\mathrm{\theta }}^{-1}\right]$

An explanation of the correct answer:

Option (b):

1. Thermal conductivity is the amount of heat that passes through a specified material per unit time, expressed as one degree per unit distance through a unit area.
2. The formula of thermal conductivity is $\mathrm{K}=\frac{∆\mathrm{Q}.∆\mathrm{x}}{∆\mathrm{t}.∆\mathrm{T}.\mathrm{A}}$, where $∆\mathrm{Q}$ is the amount of energy, $∆\mathrm{x}$ is the length, A is the cross-sectional area, $∆\mathrm{t}$ is the time, and $∆\mathrm{T}$ is the temperature.
3. The expression of thermal conductivity in the MLT system is $\mathrm{K}=\frac{\left[{\mathrm{M}}^1{\mathrm{L}}^2{\mathrm{T}}^{-2}\right]\left[\mathrm{L}\right]}{\left[\mathrm{T}\right]\left[\mathrm{\theta }\right]\left[{\mathrm{L}}^2\right]}$.
4. The final expression of thermal conductivity is $\left[{\mathrm{M}}^1{\mathrm{L}}^1{\mathrm{T}}^{-3}{\mathrm{\theta }}^{-1}\right]$.

An explanation of incorrect answer:

Option (a):

1. The time is not correct in this option for the thermal conductivity.

Option (c):

1. Both mass and temperature are calculated incorrectly.

Option (d):

1. The three parameters length, temperature, and time are determined wrong.

Therefore option b is correct.