Q142 / 200 · WBJEE 2013 · Physics

The equation of state of a gas is given by $\left(p+\frac{a}{v^{3}}\right)\left(V-b^{2}\right)=c T,$ where $p, V, T$ are pressure, volume and temperature respectively and $a, b, c$ are constants. The dimensions of $a$ and $b$ are respectively

  • Correct answer
    A
    $\left[\mathrm{ML}^{8} \mathrm{T}^{-2}\right.$ and $\left.\mathrm{L}^{3 / 2}\right]$
  • B
    $\left[\mathrm{ML}^{5} \mathrm{T}^{-2}\right.$ and $\left.\mathrm{L}^{3}\right]$
  • C
    $\left[\mathrm{ML}^{5} \mathrm{T}^{-2}\right.$ and $\left.\mathrm{L}^{6}\right]$
  • D
    $\left[\mathrm{ML}^{6} \mathrm{T}^{-2}\right.$ and $\left.\mathrm{L}^{3 / 2}\right]$

Solution

$[P]=\left[\frac{a}{V^{3}}\right] \Rightarrow\left[M L^{-1} T^{-2}\right]=\frac{a}{\left[L^{3}\right]^{3}}$ $\begin{aligned} \Rightarrow \quad a &=\left[M L^{8} T^{-2}\right] \\ &[V]=\left[b^{2}\right] \Rightarrow\left[L^{3}\right]=b^{2} \Rightarrow b=\left[L^{3 / 2}\right] \end{aligned}$

Hence, the correct answer is option: 'A'.

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