JEE MAIN - Physics (2024 - 27th January Evening Shift - No. 13)
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 $$\frac{\mathrm{a}}{\mathrm{b}^2}$$ is similar to that of :
P
RT
PV
R
Explanation
$$\begin{aligned}
& {[\mathrm{P}]=\left[\frac{\mathrm{a}}{\mathrm{V}^2}\right] \Rightarrow[\mathrm{a}]=\left[\mathrm{PV}^2\right]} \\
& \text { And }[\mathrm{V}]=[\mathrm{b}] \\
& \frac{[\mathrm{a}]}{\left[\mathrm{b}^2\right]}=\frac{\left[\mathrm{PV}^2\right]}{\left[\mathrm{V}^2\right]}=[\mathrm{P}]
\end{aligned}$$
Comments (0)
