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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physics ncert solutions class 11th Physics Class 11th Thermal Properties of Matter

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

5 months ago

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

Rise in temperature, $? T$ = 30°C

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

We can write, $\frac{? V}{V}$ = $α_{V} \times ? T$ = 49 $\times 10^{- 5} \times 30$ = 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 = 0.0147 = 1.47 $\times$ $10^{- 2}$

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This is a multiple choice answer as classified in NCERT Exemplar

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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 ?

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