Question

Density of ice is $\sigma$ and that of water is $\rho$. What will be the decrease in volume when a mass M of ice melts.
A.) $\dfrac{M}{{\sigma - \rho }}$
B.) $\dfrac{{\sigma - \rho }}{M}$
C.) $M\left[ {\dfrac{1}{\sigma } - \dfrac{1}{\rho }} \right]$
D.) $M\left[ {\dfrac{1}{\rho } - \dfrac{1}{\sigma }} \right]$

Answer 1

Hint: In these kinds of questions, the given information is used to make the equation fast and apply the volume formula .i.e. $volume = \dfrac{{mass}}{{density}}$ to find the correct option.

Complete step by step answer:

According to the given information, ice has the density $\sigma$ and density of water is $\rho$
We know that volume of matter is represented as $volume = \dfrac{{mass}}{{density}}$
Therefore the volume of ice ${V_i} = \dfrac{M}{\sigma }$ and the volume of water is ${V_w} = \dfrac{M}{\rho }$
So, the decrease in volume when the ice of mass M melts ${V_i} - {V_w} = \dfrac{M}{\sigma } - \dfrac{M}{\rho }$
$\Rightarrow {V_i} - {V_w} = M\left[ {\dfrac{1}{\sigma } - \dfrac{1}{\rho }} \right]$
Therefore the decrease in volume of ice melt $= M\left[ {\dfrac{1}{\sigma } - \dfrac{1}{\rho }} \right]$
Hence, option C is the correct option.

Note: You know that the ice density is lower than that of water, so let's figure out how, the ice density is lower than that of water because of its crystal structure, even because the hydrogen bonds between the hydrogen and oxygen atoms are longer than the covalent bonds between the water atoms are not packed close to each other thus, there are the empty spaces created in the crystal structure Of the same mass of water, this results in a greater volume of ice.