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# The density of ice is $x\,gmc{c^{ - 1}}$ and that of water is $y\,gmc{c^{ - 1}}$ . What is the change in volume in $cc$ , when $m\,gm$ of ice melts?

Last updated date: 20th Jun 2024
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Hint: Use the given formula of the volume and find the volume of the increase in the water by substituting the given values. Similarly find the volume of the decrease in the ice amount. The difference in these values gives the answer for the change in the volume of the product when the ice melts.
Useful formula:
The volume is given by
$V = \dfrac{m}{\rho }$
Where $V$ is the volume of the water or ice, $m$ is its mass and $\rho$ is its density.

Complete step by step solution:
It is given that the
The $m\,gm$ of ice melts
The density of ice is $x\,gmc{c^{ - 1}}$
The density of water is $y\,gmc{c^{ - 1}}$
We know that when the ice melts, it forms into the state of the water.
Using the formula of the volume, the volume of the water and the density is obtained as follows.
Volume of the ice reduces, $V = \dfrac{m}{x}$
The volume of the water increases, $V = \dfrac{m}{y}$
So the change in the volume is the difference of the volume of the decrease in the ice volume and the increase in the water volume.
$\Delta V = \dfrac{m}{y} - \dfrac{m}{x}$
By simplification of the above equation, we get
$\Delta V = m\left( {\dfrac{1}{y} - \dfrac{1}{x}} \right)\,cc$

Hence the change in the volume is obtained as $m\left( {\dfrac{1}{y} - \dfrac{1}{x}} \right)\,cc$ .

Note: The water commonly lies between three states as vapour in the gaseous state, water in the liquid state and ice in the solid state. The $cc$ specified in the above solution determines the cubic centimeter which is the unit of the volume.