The coefficient of volume expansion of glycerine is `49 xx 10^(-5)//^(@)C`. What is the fractional change in its density (approx.) for `30^(@)C` rise in temperature?

Explanation

Coefficient of volume expansion of glycerin, `α_(V) = 49 × 10^(–5) K^(–1)`
Rise in temperature, `ΔT = 30^(@)C`
Fractional change in its volume `=(DeltaV)/(V)`
This change is related with the change in temperature as:
`(DeltaV)/(V)=a_(V)DeltaT`
`V_(T2)-V_(T1)=V_(T1)a_(V)DeltaT`
`(m)/(P_(T2))-(m)/(P_(T1))=(m)/(P_(T1))a_(v)DeltaT`
Where,
m = Mass of glycerine
`P_(r1)`=Initial density at `T_(1)`
∴Fractional change in the density of glycerin = 49 ×10–5 × 30 = 1.47 × 10–2`P_(r_(2))"= Final density at" T_(2)`
`(P_(r_(1))-P_(r_(2)))/(P_(r_(2)))a_(v)DeltaT`
Where,
`(P_(r_(1))-P_(r_(2)))/(P_(r_(2)))`=Fraction change in density
∴Fractional change in the density of glycerin `= 49 ×10^(–5) × 30 = 1.47 × 10^(–2)`