Question

When the ice melts, its volume _________
(A) Increases
(B) Decreases
(C) Does not change
(D) Can’t say

Answer 1

Hint : To solve this problem, you have to remember the fact that ice floats in water. That happens due to the reason that the density of ice is less than the density of water. With this, we use the law of conservation of mass, i.e. mass of water will be equal to the mass of ice that melts.

Formula used:
The formula for mass density is given as,
 $ \rho = \dfrac{M}{V} $
where, $ \rho $ is the density of the substance, $ M $ is the mass of the substance, $ V $ is the volume taken.

Complete step by step answer
It is a well-known fact that the density of ice is less than the density of water and it is the reason why icebergs float.
According to the law of conservation of mass, mass can neither be created nor be destroyed.
Now, for example, if $ 10g $ ice melts into water. The weight of the water will also be $ 10g $ , i.e. the mass of ice will be equal to the mass of water. Or, we can say that if ice had $ N $ no. of molecules before melting, water will also have $ N $ no. of molecules.
The density of ice is less, physically this means that the molecules are further away from each other.
In the case of water, its density is more than ice. Thus the molecules are closer to each other. Since the molecules of ice are further away, $ N $ no. of molecules will take up more volume as compared to water.
We can check this mathematically,
We know that the formula for mass density is given as
 $ \Rightarrow\rho = \dfrac{M}{V} $
 $ \Rightarrow \rho V = M $
For ice, we can write
 $ \Rightarrow{\rho _i}{V_i} = M $
For water,
 $ \Rightarrow{\rho _w}{V_w} = M $
On the right-hand side, we have a mass of ice and water. But the mass remains the same. Thus RHS of these equations is equal. So, we can write
 $ \Rightarrow{\rho _i}{V_i} = {\rho _w}{V_w} $
 $ \Rightarrow \dfrac{{{\rho _i}}}{{{\rho _w}}} = \dfrac{{{V_w}}}{{{V_i}}} $
We know that,
 $ \Rightarrow {\rho _i} < {\rho _w} $
 $ \Rightarrow {V_i} > {V_w} $
Thus, the volume occupied by the ice is more compared to the volume occupied by the same amount of water. So when an ice cube melts, its volume decreases.
Thus, option (B) is correct.

Note
Be careful about the fact that only mass is conserved or remains the same in such processes. While volume and density can change. Mathematically, volume and density will change in such a way that the law of conservation of mass is valid.