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

Given: The coefficient of volume expansion is 49× 10 −5   K −1 and the change in temperature is 30 °C.

The fractional change in volume with temperature is given as,

ΔV V = α V ΔT V T 2 − V T 1 = V T 1 α V ΔT (1)

The volume is given as,

V= m ρ (2)

Where, m is the mass and ρ is the density.

From equation (1) and (2), we get

( m ρ T 2 )−( m ρ T 1 )=( m ρ T 1 ) α V ΔT ρ T 1 − ρ T 2 ρ T 2 = α V ΔT

By substituting the given values in the above expression, we get

ρ T 1 − ρ T 2 ρ T 2 =49× 10 −5 ×30 =1.47× 10 −2 =0.0147

Thus, the fractional change in density of the Glycerin is 0.0147.