Question

Energy density is defined as energy per unit volume. Determine the dimensional formula for energy density.

Answer 1

Step 1: Given data:
Mathematically,
$Energydensity=\frac{Energy}{Volume}$

Step 2: Substitute the dimensional formulae of energy and volume in the formula:
We know that the dimensions of energy and volume are as follows:
$$\begin{gathered} Energy=\left[M{L}^2{T}^{-2}\right] \\ Volume=\left[L^3\right] \end{gathered}$$
On substituting in the given formula, we get:
$$\begin{gathered} [EnergyDensity]=\frac{\left[Energy\right]}{\left[Volume\right]} \\ =\frac{\left[M{L}^2{T}^{-2}\right]}{{[L}^3]} \\ =\left[M{L}^2{T}^{-2}\right]\left[L^{-3}\right] \\ =\left[M{L}^{2-3}{T}^{-2}\right] \\ =\left[M{L}^{-1}{T}^{-2}\right] \end{gathered}$$

Thus, the dimensional formula for energy density is $\left[M{L}^{-1}{T}^{-2}\right]$.