What is dimensions of $a$ in van der Waals' equation?

[M L^{- 1} T^{- 2}]

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[M L^{5} T^{- 2}]

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[M L^{3} T^{- 2}]

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[M^{2} L^{3} T^{- 2}]

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Solution

The correct option is B $[M L^{5} T^{- 2}]$
Principle of homogeneity of dimensions and only like quantities can be added or subtracted from each other.
van der Waals' equation is
$(p + \frac{a}{V^{2}}) (V - b) = R T$
Here,
Dimensions of $\frac{a}{V^{2}} =$ Dimensions of $p$ ,
Dimensions of $a =$ Dimensions of $[p V^{2}]$
$= [M L^{- 1} T^{- 2}] {[L^{3}]}^{2}$
$= [M L^{5} T^{- 2}]$

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What is dimensions of a in van der Waals' equation?

The correct option is B [ML5T−2]Principle of homogeneity of dimensions and only like quantities can be added or subtracted from each other.van der Waals' equation is(p+aV2)(V−b)=RTHere,Dimensions of aV2= Dimensions of p,Dimensions of a= Dimensions of [pV2] =[ML−1T−2][L3]2 =[ML5T−2]

What is dimensions of $a$ in van der Waals' equation?