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Q. 11.11 The coefficient of volume expansion of glycerine is 49\times 10^{-5}K^{-1}.What is the fractional change in its density for a 30^{\circ}C rise in temperature?

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Coefficient of volume expansion of glycerine is \gamma =49\times 10^{-5}K^{-1}

Let initial volume and mass of a certain amount of glycerine be V and m respectively.

Initial density is 

\rho =\frac{m}{V}

Change in volume for a 30 oC rise in temperature will be

\\\Delta V=V(\gamma \Delta T)\\ \Delta V=V(49\times 10^{-5}\times 30)\\ \Delta V=0.0147V

Final Density is

\\\rho' =\frac{m}{V+\Delta V}\\ \rho'=\frac{m}{1.0147V}\\ \rho'=\frac{0.986m}{V}

Fractional Change in density is 

\\\frac{\rho'-\rho}{\rho}\\ =\frac{\frac{0.986m}{v}-\frac{m}{v}}{\frac{m}{v}}\\ =-0.014

The negative sign signifies with an increase in temperature density will decrease.

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