The coefficient of volume expansion of glycer | vedclass

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(A) Given: Coefficient of volume expansion $\gamma = 49 	imes 10^{-5} \, K^{-1}$ and change in temperature $\Delta T = 30^{\circ} C = 30 \, K$.The de

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$1.47 	imes 10^{-2}$

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(A) Given: Coefficient of volume expansion $\gamma = 49 	imes 10^{-5} \, K^{-1}$ and change in temperature $\Delta T = 30^{\circ} C = 30 \, K$.The density $ho$ of a substance at temperature $T + \Delta T$ is given by $ho_2 = \frac{ho_1}{1 + \gamma \Delta T} \approx ho_1(1 - \gamma \Delta T)$ for small values of $\gamma \Delta T$.Rearranging the terms,we get $\frac{ho_1 - ho_2}{ho_1} = \gamma \Delta T$.The fractional change in density is $\frac{\Delta ho}{ho_1} = \gamma \Delta T$.Substituting the values: $\frac{\Delta ho}{ho_1} = (49 	imes 10^{-5}) 	imes 30 = 1470 	imes 10^{-5} = 1.47 	imes 10^{-2}$.

The coefficient of volume expansion of glycerin is $49 \times 10^{-5} \, K^{-1}$. The fractional change in the density on a $30^{\circ} C$ rise in temperature is ..........

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