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Physics · UNITS AND MEASUREMENT
हिन्दीThe van der Waals equation for a real gas is given by \( (P + \frac{a}{V^2})(V - b) = RT \), where \( P \) is pressure, \( V \) is volume, and \( T \) is temperature. The dimensional formula for the ratio \( \frac{a}{b^2} \) is:
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Correct answer · Option B
\( [\text{M L}^{-1} \text{T}^{-2}] \)
Explanation
By the principle of homogeneity, \( [a/V^2] = [P] \implies [a] = [M L^{-1} T^{-2}][L^6] = [M L^5 T^{-2}] \). Also, \( [b] = [V] = [L^3] \). Hence, \( [a/b^2] = \frac{[M L^5 T^{-2}]}{[L^6]} = [M L^{-1} T^{-2}] \), which has the dimensions of pressure.
