AP EAMCET · PHYSICS · Thermodynamics
The van der Waals' equation for a gas is
\[
\left(P+\frac{a}{V^2}\right)(V-b)=n R T
\]
where \(P, V, R, T\) and \(n\) represent the pressure, volume, universal gas constant, absolute temperature and number of moles of a gas, respectively. \(a\) and \(b\) are constants.
The ratio \(\frac{b}{a}\) will have the following dimensional formula.
- A \(\left[\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2\right]\)
- B \(\left[\mathrm{M}^{-1} \mathrm{~L}^{-1} \mathrm{~T}^{-1}\right]\)
- C \(\left[\mathrm{ML}^2 \mathrm{~T}^2\right]\)
- D \(\left[\mathrm{MLT}^{-2}\right]\)
Answer & Solution
Correct Answer
(A) \(\left[\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2\right]\)
Step-by-step Solution
Detailed explanation
van der Waals gas equation is \[ \left(p+\frac{a}{V^2}\right)(V-b)=n R T \] From principle of homogeneity Dimension of \(\frac{a}{V^2}=\) dimension of \(P\) \(\therefore\) Dimension of \(a=\left[V^2\right] \times[P]\)…
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