Question

The coefficient of volume expansion of a liquid is 49´10-5
/
0
K. Calculate the fractional change in its density when the temperature is raised by 300
C.

Answer 1

Explanation:

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

Where,

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.