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Home » The coefficient of volume expansion of glycerine is . What is the fractional change in its density for a 30 °C rise in temperature?
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?
CBSE | Class 11 | NCERT | Thermal Properties of Matter
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?

Given:

Coefficient of volume expansion of glycerine, \alpha_{v}=49 \times 10^{-5} \mathrm{~K}^{-1}

Rise in temperature, \Delta \mathrm{T}=30^{\circ} \mathrm{C}

Fractional change in volume =\frac{\Delta V}{V}

We know that,

\alpha_{\mathrm{V}} \Delta \mathrm{T}=\frac{\Delta V}{V}

Which can also be written as,  V_{T_{2}}-V_{T_{1}}=V_{T_{1}} \alpha_{v} \Delta T

If taken relation into consideration we have,

\frac{m}{\rho T_{2}}-\frac{m}{\rho T_{1}}=\frac{m}{\rho_{T_{1}}} \alpha_{v} \Delta T

Where, \mathrm{m}= mass of glycerine

\rho_{T_{2}}= Final density at \mathrm{T}_{2}

\rho_{T_{1}}= Initial density at \mathrm{T}_{1}

\Rightarrow \frac{\rho_{T_{1}}-\rho T_{2}}{\rho_{T_{2}}}= Fractional change in density

Therefore, Fractional change in density =1.47 \times 10^{-2}

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