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Mass of a substance is changing with respect to its volume as m = -v3 + 3v2 -2v, what is the maximum specific gravity of the substance between v = 1 m3 and v = 2 m3? (Density of reference substance = 0.25 kg/m3)

Mass of a substance is changing with respect to its volume as m = -v3 + 3v2 -2v, what is the maximum specific gravity of the substance between v = 1 m3 and v = 2 m3? (Density of reference substance = 0.25 kg/m3) Correct Answer 1

Density of substance D = m/v = -v2 + 3v – 2, => Specific gravity of substance S = D/0.25 = 4(-v2 + 3v – 2), => dS/dv = 4(-2v + 3) = 0, => v = 1.5, => S is maximum at v = 1.5, => maximum specific gravity = 4(-1.52 + 3*1.5 – 2) = 1.

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