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The value of coefficient of volume expansion of glycerin is $5\times10^{-4}$ $K^{-1}$. The fractional change in the density of glycerin for a rise of $40^\circ C$ in its temperature, is:
A
0.010
B
0.015
C
0.020
D
0.025
Detailed Solution
$d_f = \frac{d_i}{1 + \gamma\Delta T}$
Fractional change $= \frac{d_i - d_f}{d_i} = 1 - (1 + \gamma\Delta T)^{-1} \approx \gamma\Delta T$
$= 5\times10^{-4}\times 40 = 0.020$
Fractional change $= \frac{d_i - d_f}{d_i} = 1 - (1 + \gamma\Delta T)^{-1} \approx \gamma\Delta T$
$= 5\times10^{-4}\times 40 = 0.020$