ગ્લિસરિન માટે કદ-પ્રસરણાંક $49 \times10^{-5}\, K^{-1}$ છે. જો તેનાં તાપમાનમાં $30 \,^oC$ નો વધારો કરવામાં આવે, તો તેની ઘનતામાં થતો આંશિક ફેરફાર કેટલો હશે ?

Coefficient of volume expansion of glycerin, $\alpha_V=49 \times 10^{-5} K ^{-1}$

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

Fractional change in its volume $=\frac{\Delta V}{V}$ This change is related with the change in temperature as:

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

$V_{T_{2}}-V_{T_{1}}=V_{T_{1}} \alpha_{V} \Delta T$

$\frac{m}{\rho_{T_{2}}}-\frac{m}{\rho_{T_{1}}}=\frac{m}{\rho_{T_{1}}} \alpha_{V} \Delta T$

Where, $m=$ Mass of glycerine

$\rho_{T_{1}}=$ Initial density at $T_{1}$

$\rho_{r_{1}}=$ Final density at $T_{2}$

$\frac{\rho_{T_{1}}-\rho_{T_{2}}}{\rho_{T_{2}}}=\alpha_{V} \Delta T$

Where,

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

$\therefore$ Fractional change in the density of glycerin $=49 \times 10^{-5} \times 30=1.47 \times 10^{-2}$