Answer :

Given,

Coefficient of volume expansion of glycerin, αV = 49 × 10–5 K–1


Rise in temperature, ΔT = 30°C = 30 K


Fractional change in its volume = ΔV/V


We know,


ΔV/V = αVΔT


VT2 - VT1 = VT1αVΔT


(m/ρT2)-(m/ρT1) = (m/ρT1VΔT


[(1/ρT2)-(1/ρT1)]/(1/ρT1) = αVΔT


T1 - ρT2)/ρT2 = αVΔT


Where, m is the mass of glycerin


ρT1 is the initial density at T1


ρT2 is the initial density at T2


T1 - ρT2)/ρT2 is the fractional change in density


So, fractional change in density of glycerine = 49 × 10–5 K–1 × 30 K


= 1.47 × 10-2


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