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Q.

The van der Waal's equation for a gas is P+aV2(V-b)=nRT 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 b/a will have the following dimensional formula

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a

M-1 L-1 T-1

b

MLT-2

c

ML2 T2

d

M-1 L-2 T2

answer is A.

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Detailed Solution

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P+aV2(V-b)=nRT 
According to principle of Homogeneity 'b' has the same dimensions of 'V'
b = L3
similarly aV2 has same dimensions of 'P'

a L32=ML-1 T-2a=ML-1 T-2L6 a=ML5 T-2ba=L3ML5 T-2=M-1 L-2 T2

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