Q.11:- The coefficient of volume expansion of glycerin is 49 × 10–5 K–1. What is the fractional change in its density for a 30 °C rise in temperature?
Coefficient of volume expansion of glycerin, αV = 49 × 10–5 K–1
Rise in temperature, ΔT = 30°C
Fractional change in its volume = ΔV/V
This change is related with the change in temperature as:
ΔV/V = αV ΔT
VT2 – VT1 = VT1 αV ΔT
(m /ρT2)- (m /ρT1) = (m /ρT1)αV ΔT
m = Mass of glycerine
ρT1 = Initial density at T1
ρT2 = Initial density at T2
(ρT1 – ρT2 ) / ρT2 = Fractional change in density
∴ Fractional change in the density of glycerin = 49 ×10–5 × 30 = 1.47 × 10–2.