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