Question

The coefficient of volume expansion of glycerine is 49 × 10–5 K–1. What is the fractional change in its density for a 30 °C rise in temperature?

Answer 1

Coefficient of volume expansion of glycerin, αV = 49 × 10–5 K–1
Rise in temperature, ΔT = 30°C
Fractional change in its volume = $\frac{ΔV}{V}$
This change is related to the change in temperature:
$\frac{ΔV}{V}$ = αVΔT
VT2 -VT1 = VT1αVΔT
$\frac{m}{\rho}$T2 - $\frac{m}{\rho}$T1 = $\frac{m}{\rho}$T1αVΔT
Where,
m = Mass of glycerine
ρT1 = Initial density at T1
ρT2 = Final density at T2
$\frac{ρT_1 - ρT_2}{ρT_2}$ = αVΔT
Where,
$\frac{ρT_1 - ρT_2}{ρT_2}$ = Fractional change in density
∴ Fractional change in the density of glycerin = 49 ×10–5 × 30 = 1.47 × 10–2