Question 363: Properties of Matter

Question

The value of coefficient of volume expansion of glycerin is 5 $$ 	imes $$ 10
$$-$$4
K
$$-$$1
. The fractional change in the density of glycerin for a rise of 40
o
C in its temperature, is

Accepted Answer

Let r
0
and r
T
be densities of glycerin at 0ÃÂ°C and TÃÂ°C respectively. Then,
$${ho _T} = {ho _0}\left( {1 - \gamma \Delta T} ight)$$
where $$\gamma $$ is the coefficient of volume expansion of glycerine and $${\Delta T}$$ is rise in temperature.
$${{{ho _T}} \over {{ho _0}}} = 1 - \gamma \Delta T \Rightarrow \gamma \Delta T = 1 - {{{ho _T}} \over {{ho _0}}}$$
Thus, $${{{ho _0} - {ho _T}} \over {{ho _0}}} = \gamma \Delta T$$
Here, $$\gamma  = 5 	imes {10^{ - 4}}{K^{ - 1}}$$ and $$\Delta T = {40^o}C = 40K$$
$$ 	herefore $$ The fractional change in the density of glycerin
$$ = {{{ho _0} - {ho _T}} \over {{ho _0}}} = \gamma \Delta T = \left( {5 	imes {{10}^{ - 4}}{K^{ - 1}}} ight)\left( {40K} ight) = 0.020$$

Answer

0.025

Answer

0.010

Answer

0.015

Answer

0.020

Properties of Matter

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 o C in its temperature, is

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