**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 ?**

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Payal Gupta | Contributor-Level 10

8 months ago

11.11 Coefficient of volume expansion of glycerin, $α_{V}$ = 49 $* 10^{- 5}$ /K

Rise in temperature, $? T$ = 30°C

Fractional change in volume = $\frac{? V}{V}$

We can write, $\frac{? V}{V}$ = $α_{V} * ? T$ = 49 $* 10^{- 5} * 30$ = 0.0147 ……(i)

If the final volume is $V_{2}$ and initial volume is $V_{1}$ , then

$\frac{? V}{V}$ = $\frac{V_{2} - V_{1}}{V_{1}}$

$V_{2} = \frac{m}{ρ_{2}}$ and $V_{1} = \frac{m}{ρ_{1}}$ where $ρ_{1}$ & $ρ_{2}$ are initial and final densities

$\frac{? V}{V}$ = $\frac{V_{2} - V_{1}}{V_{1}}$ = $\frac{ρ_{2} - ρ_{1}}{ρ_{1}}$ = fractional change in density = 0

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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 ?