Thermal Properties of Matter NCERT Solutions Class 11 Physics - Solved Exercise Question 11.11

Question 11.11:
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?
Solution:
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)- (/ρT1) = (/ρT1)αV ΔT
Where,
m = Mass of glycerine
ρT1 = Initial density at T1
ρT2 = Initial density at T2
T1 - ρT2 ) / ρT2  =  Fractional change in density
∴Fractional change in the density of glycerin = 49 ×10–5 × 30 = 1.47 × 10–2

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