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?
Correct option is A) Let V0 be the initial volume of glycerine, i.e., at 0oC (dry). If Vt be its volume at 30oC. Then Vt=V0(1+vΔt) =V0(1+49×10−5×30) Vt=V0(1+0.01470)=1.0147070V0 ⇒VtV0=1.014701 Let ρ0 and ρt be the initial and final densities of glycerine then initial density, ρ0=v0m and final density, ρt=Vtm where, m= mass of glycerine ρ0Δρ= ρ0ρt−ρ0=V0mm(Vt1−V01)=(VtV0−1) ⇒Δρ0Δρ=(1.014701−1)=−0.0145 Here, negative sign shows that density decreases with rise in temperature. ρ0Δρ=0.0145=1.45×10−2 ⇒Δρ0Δρ=1.5×10−2
