Question

What is the dimensional formula for thermal resistance?

Answer 1

Definition:

Thermal resistance would be a thermal attribute that measures the variation between temperatures wherein the passage of heat is impeded by an item or substance.

Dimension formula:

This same thermal resistance is inversely proportional to thermal conductance.

Mathematically, dimension can be represented as:

$\mathrm{Thermal}\mathrm{resistance}=\frac{\mathrm{Temperature}\mathrm{difference}}{\mathrm{Thermal}\mathrm{current}}$

$$\begin{gathered} =\frac{∆\mathrm{T}}{\left({\displaystyle \frac{∆\mathrm{Q}}{∆\mathrm{t}}}\right)} \\ =\frac{\left[\mathrm{K}\right]}{\left({\displaystyle \frac{\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]}{\left[\mathrm{T}\right]}}\right)} \\ =\frac{\left[\mathrm{K}\right]\left[\mathrm{T}\right]}{\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]} \\ =\left[{\mathrm{M}}^{-1}{\mathrm{L}}^{-2}{\mathrm{T}}^3\mathrm{K}\right] \end{gathered}$$

Therefore, the dimensional formula for thermal resistance will be $\left[{\mathrm{M}}^{-1}{\mathrm{L}}^{-2}{\mathrm{T}}^3\mathrm{K}\right]$.