### 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?

**Answer:-**

Coefficient of volume expansion of glycerin, *α*_{V} = 49 × 10^{–5} K^{–1}

Rise in temperature, Δ*T *= 30°C

Fractional change in its volume = Δ*V*/*V*

This change is related with the change in temperature as:

Δ*V*/*V* = *α*_{V} Δ*T*

*V*_{T2} – *V*_{T1} = *V*_{T1} α_{V} Δ*T*

(*m* /ρ_{T2})- (*m* /ρ_{T1}) = (*m* /ρ_{T1})*α _{V} ΔT*

Where,

*m*= Mass of glycerine

ρ

_{T1}= Initial density at

*T*1

ρ

_{T2}= Initial density at

*T*2

(ρ

_{T1}– ρ

_{T2 }) / ρ

_{T2}= Fractional change in density

∴ Fractional change in the density of glycerin = 49 ×10

^{–5 }× 30 = 1.47 × 10

^{–2}.