On heating a liquid of coefficient of cubical expansion ? in a container having coefficient of...

Question:

On heating a liquid of coefficient of cubical expansion {eq}\gamma{/eq} in a container having coefficient of linear expansion {eq}\frac{\gamma}{3}{/eq}.

The level of liquid in the container will{eq}\rule{3cm}{0.15mm}{/eq}.

Coefficient of linear expansion:

The term coefficient of expansion can be defined as when the temperature of the rod is changing, then the length of the rod also changes from its original length. It is denoted by the Greek letter {eq}\alpha {/eq}.

Given data:

• The coefficient of the linear expansion is {eq}{\gamma _s} = \dfrac{\gamma }{3} {/eq}

As from the given data the liquid is heating in a container, then the volume expansion becomes

{eq}\alpha = 3 \times {\gamma _s} {/eq}

Substituting the values in the above equation as,

{eq}\begin{align*} \alpha &= 3 \times {\gamma _s}\\ \alpha &= 3 \times \dfrac{\gamma }{3}\\ \alpha &= \gamma \end{align*} {/eq}

As the coefficient of the cubical expansion of liquid equal to the coefficient of the cubical expansion of the vessel, this means or implies that the level of liquid in the container will not change on heating.