Value of coefficient of volume expansion of glycerin is 5 × 10^{-4}, K^{-1} . fractional change in

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10-1.Thermometry, Thermal Expansion and Calorimetry

normal

The value of coefficient of volume expansion of glycerin is $5 \times 10^{-4}\, K^{-1}$. The fractional change in the density of glycerin for a rise of $40\,^oC$ in its temperature, is

A

$0.010$

B

$0.015$

C

$0.020$

D

$0.025$

Solution

$\mathrm{d}_{\mathrm{f}}=\frac{\mathrm{d}_{\mathrm{i}}}{(1+\gamma \Delta \mathrm{T})}$

fractional change

$=\frac{\mathrm{d}_{\mathrm{i}}-\mathrm{d}_{\mathrm{f}}}{\mathrm{d}_{\mathrm{i}}}=1-\frac{\mathrm{d}_{\mathrm{f}}}{\mathrm{d}_{\mathrm{i}}}$

$=1-(1+\gamma \Delta \mathrm{T})^{-1}$

$\because(1+\mathrm{x})^{\mathrm{n}} \approx 1+\mathrm{nx}$

$=\gamma \Delta \mathrm{T}$

$=5 \times 10^{-4} \times 40$

$=0.020$

Standard 11

Physics

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