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The equation of state of a gas is given by P+aV3V−b2=cT, where P, V, T are pressure, volume and temperature respectively, and a, b, c are constants. The dimensions of a and b are respectively

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a

ML8 T-2 and L3/2

b

ML5 T-2 and L3

c

ML5 T-2 and L6

d

ML6 T-2 and L3/2

answer is A.

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Detailed Solution

Given, P+aV3V-b2=cTDimensions of aV3=Dimensions of P∴ Dimensions of a = dimensions of PV3[a]=FAV3 ∵P=FA=MLT-2L2×L33=ML8 T-2Dimensions of b2= dimensions of V∴ [b]=[V]1/2=L31/2 or [b]=L3/2

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