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Question: In Vander Waal's equation\(\left\lbrack P + \frac{a}{V^{2}} \right\rbrack(V - b) = RT,\) the dimensi...

In Vander Waal's equation[P+aV2](V−b)=RT,\left\lbrack P + \frac{a}{V^{2}} \right\rbrack(V - b) = RT, the dimensions of a are

A

M1L5T−2M^{1}L^{5}T^{- 2}

B

M0L2T−3M^{0}L^{2}T^{- 3}

C

M1L3T−2M^{1}L^{3}T^{- 2}

D

M1L1T−2M^{1}L^{1}T^{- 2}

Answer

M1L5T−2M^{1}L^{5}T^{- 2}

Explanation

Solution

According to the principle of homogeneity dimensional of P = Dimension of aV2\frac{a}{V^{2}}

Ž a[L3]2=[ML−1T−1]\frac{a}{\lbrack L^{3}\rbrack^{2}} = \lbrack ML^{- 1}T^{- 1}\rbrack Ž a=[ML5L−2]a = \lbrack ML^{5}L^{- 2}\rbrack