# A density bottle contains 104.5 g of a liquid at 34^oC on heating it to 100^oC, the mass of the...

## Question:

A density bottle contains 104.5 g of a liquid at 34{eq}^o {/eq}C on heating it to 100{eq}^o {/eq}C, the mass of the liquid expelled is 4.5 g. Find the coefficient of apparent expansion of liquid.

## Thermal Expansion:

The thermal expansion is property of a material by virtue of which it changes its apparent figure corresponding to the temperature variation. Generally, it is represented in the form of per Kelvin. This phenomenon occurs due to the variation in the molecular energy of the material.

Given data

• The mass of liquid in bottle is {eq}m = 104.5\;{\rm{g}} {/eq}.
• The initial temperature is {eq}{T_1} = 34^\circ {\rm{C}} {/eq}.
• The final temperature is {eq}{T_2} = 100^\circ {\rm{C}} {/eq}.
• The mass of expelled liquid is {eq}\Delta m = 4.5\;{\rm{g}} {/eq}.

The expression for the coefficient of apparent expansion is,

{eq}\alpha = \dfrac{{\Delta m}}{{m\left( {{T_2} - {T_1}} \right)}} {/eq}

Substitute values.

{eq}\begin{align*} \alpha &= \dfrac{{4.5\;{\rm{g}}}}{{\left( {104.5\;{\rm{g}}} \right)\left( {100^\circ {\rm{C}} - 34^\circ {\rm{C}}} \right)}}\\ &= \dfrac{{4.5\;{\rm{g}}}}{{\left( {104.5\;{\rm{g}}} \right)\left( {66^\circ {\rm{C}}} \right)}}\\ &= 6.52 \times {10^{ - 4}}\;^\circ {{\rm{C}}^{ - 1}} \end{align*} {/eq}

Thus, the coefficient of apparent expansion is {eq}6.52 \times {10^{ - 4}}\;^\circ {{\rm{C}}^{ - 1}} {/eq}.