Chapter 19, Problem 44A

When an ice cube in a glass of water melts, does the water level in the glass rise, fall, or remain unchanged? Does your answer change if the ice cube contains many air bubbles? Does your answer change if the ice cube contains many grains of heavy sand?

To determine

To explain:Whether the water level in glass rise, fall or remain unchanged when ice cube in glass of water melts.

To identify: Whether the answer will change if there are air bubbles in ice cube. Also, whether the answer will change if there are heavy sand grains in an ice cube.

Explanation of Solution

Introduction:

Water is one of the basic elements of living things. On earth there are around 70% of water. Water can be found in one of the three forms, liquid, solid or gases. The major difference between its three state is the distance between its molecule.

According to the Archimedes’ principle, when body is partially or completely submerged in the fluid, the buoyant force acting on it. The magnitude of the buoyant force is equal to the weight of the fluid displaced by the body. When ice is melted in the water glass it acquires the volume of glass. But density of the ice is less than the density of water. From basic definition of density,

  $\begin{array}{l}{\sigma }_{water}=\frac{m}{V_{water}}\\ \text{And}\\ {\sigma }_{ice}=\frac{m}{V_{ice}}\\ \text{But,}\\ {\sigma }_{ice}<{\sigma }_{water}\\ \text{Therefore,}\\ V_{water}<V_{ice}\end{array}$

Therefore, the water level after the ice cube melting is decreases. When ice contain many air bubbles, in that case density of ice cube is less than the density of water which results into the decrease in the level of water.

If ice cube contains many grains of heavy sand, after the melting of the ice, sand grain has higher density than the water. So, it has more mass than the same volume of water. Since before melting of ice + sand grain it floating on the water surface. So, water level in glass will increases after the melting of ice cube containing sand grain.

Conclusion:

Therefore, the water level in glass decreases when ice cube is melting. Similarly, when ice cube contains air pores, after the melting of ice, water level fall down. Whereas when ice cube contains sand grain in that case also water level increases after the melting of ice.