Units And Dimensions Question 3
Question 3 - 2024 (27 Jan Shift 2)
The equation of state of a real gas is given by $\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^{2}}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where $\mathrm{P}, \mathrm{V}$ and $\mathrm{T}$ are pressure. volume and temperature respectively and $\mathrm{R}$ is the universal gas constant. The dimensions of $\frac{a}{b^{2}}$ is similar to that of :
(1) PV
(2) $\mathrm{P}$
(3) RT
(4) $\mathrm{R}$
Show Answer
Answer: (2)
Solution:
$[\mathrm{P}]=\left[\frac{\mathrm{a}}{\mathrm{V}^{2}}\right] \Rightarrow[\mathrm{a}]=\left[\mathrm{PV}^{2}\right]$
And $[\mathrm{V}]=[\mathrm{b}]$
$\frac{[\mathrm{a}]}{\left[\mathrm{b}^{2}\right]}=\frac{\left[\mathrm{PV}^{2}\right]}{\left[\mathrm{V}^{2}\right]}=[\mathrm{P}]$
