Question

When water freezes its volume increases by $4\%$. What volume of water is required to make $221$${\text{c}}{{\text{m}}^3}$ of ice?

Answer 1

Hint: Here we are given the percentage increase in volume of ice. Assuming an unknown variable for volume of water, we can add the increase in the volume to it and equate it to the required volume. Solving the obtained equation for the unknown variable, we can get the required volume for water.

Complete step by step answer: Given that the volume of water increases by $4\% $, when we freeze it and
we are required to find the volume of water required to make $221{\text{c}}{{\text{m}}^3}$ of ice.
Now let us assume an unknown variable for the volume of water required to make ice which has volume of $221{\text{c}}{{\text{m}}^3}$
Let the volume of water required by\[\]. Since in ice form, the volume is $4\% $ more than the volume in liquid state, we can write the following expression for volume, taking into consideration the volume of ice that we need to obtain
${\text{x + 4 $\%$ of x = 221c}}{{\text{m}}^3}$
$\Rightarrow$ ${\text{x}} + \dfrac{{{\text{4x}}}}{{100}} = 221$
Cross multiplying and solving the equation,
$\Rightarrow$ $\dfrac{{100{\text{x + 4x}}}}{{100}} = 221$
$\Rightarrow$ $\dfrac{{104{\text{x}}}}{{100}} = 221$
$ \Rightarrow {\text{x = 221}} \times \dfrac{{100}}{{104}}$
${\text{x = 212}}{\text{.5 c}}{{\text{m}}^3}$
Thus we got the volume of water required to make of $221 cm^{3}$ ice = $221.5cm^{3}$

Additional Information: The freezing point describes the liquid to solid transition while the melting point is the temperature at which water goes from a solid (ice) to liquid water. In theory, the two temperatures would be the same, but liquids can be supercooled beyond their freezing point. Ordinarily, the freezing point of water and melting point is $0^{o}C$ or $32\,{\text{F}}$. The temperature may be lower if supercooling occurs.

Note: When matter is cooled, it contracts while when it is heated, it expands. But here we are saying that the volume of water increases when temperature is lowered. The reason behind this anomaly is the lattice structure of ice. The lattice of ice is such that there are many empty spaces between the molecules which leads to an increase in volume on freezing water.