Question:
What would be the SI unit for the quantity $\rho V^{2} T^{2} / n ?$
Solution:
The SI unit for pressure, p is Nm–2.
The SI unit for volume, V is m3.
The SI unit for temperature, T is K.
The SI unit for the number of moles, n is mol.
Therefore, the SI unit for quantity $\frac{p V^{2} T^{2}}{n}$ is given by,
$=\frac{\left(\mathrm{Nm}^{-2}\right)\left(m^{3}\right)^{2}(\mathrm{~K})^{2}}{\mathrm{~mol}}$
$=\mathrm{Nm}^{4} \mathrm{~K}^{2} \mathrm{~mol}^{-1}$