WBJEE · Physics · Units and Dimensions
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
- 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 \(\left.\mathrm{L}^{3 / 2}\right]\)
Answer & Solution
Correct Answer
(A) \(\left[\mathrm{ML}^{8} \mathrm{T}^{-2}\right.\) and \(\left.\mathrm{L}^{3 / 2}\right]\)
Step-by-step Solution
Detailed explanation
\([P]=\left[\frac{a}{V^{3}}\right] \Rightarrow\left[M L^{-1} T^{-2}\right]=\frac{a}{\left[L^{3}\right]^{3}}\)…
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