Question

Ice pieces are floating in a beaker A containing water and also in a beaker B containing miscible liquid of specific gravity \(1.2\) Ice melts the level of (A) water increases in \(\mathrm{A}\) (B) water decreases in \(\mathrm{A}\) (C) Liquid in B decrease B (D) Liquid in B increase

Short answer

Upon melting, the ice in beaker A does not change the water level, because the volume of the melted ice equals the volume of the water initially displaced by the ice. In beaker B, the level of liquid increases when the ice melts, because the volume of water formed from melted ice is larger than the initially displaced liquid volume. Hence, the correct answer is (D), "Liquid in B increases."

Step-by-step solution

Establish the Buoyancy Principle for Ice in Water

When the ice is floating in water, it displaces an amount of water that weighs the same as the ice. Upon melting, the volume of the melted ice equals the volume of the water it had initially displaced. Therefore, the level of water in beaker A will remain the same; it will neither increase nor decrease.

Establish the Buoyancy Principle for Ice in a Miscible Liquid

When the ice floats in the liquid with a specific gravity of 1.2, it will displace a volume of liquid equal to the weight of the ice divided by the specific gravity of the liquid. Now, when the ice melts, it adds a volume of water equivalent to its volume while it was frozen (because water expands upon freezing, hence the density lowers, and its volume increases). The weight of the ice remains the same, but due to the lower specific gravity of water (1.0) compared to the 1.2 of the miscible liquid, the volume of water formed by the melting ice is greater than the volume of the miscible liquid it had initially displaced.

Conclude on the Level of Liquid in Each Beaker

The melting of ice in beaker A should neither increase nor decrease the water level. Thus, the answers (A), "water increases in A," and (B), "water decreases in A," are incorrect. When ice melts in beaker B, it adds a volume of water that is greater than the originally displaced volume of miscible liquid, i.e., the level of liquid in B increases. Hence, the answer is (D), "Liquid in B increases." The answer (C), "Liquid in B decreases," is not right because the volume of water formed from melted ice is larger than the initially displaced liquid volume.

Key concepts

Specific Gravity

Specific gravity is a crucial concept in understanding buoyancy and flotation. It is defined as the ratio of the density of a substance to the density of a reference substance, typically water for liquids. Specifically, the formula is:

• \[\text{Specific Gravity} = \frac{\text{Density of the Substance}}{\text{Density of Water}}\]

In this exercise, the specific gravity of the miscible liquid in beaker B is 1.2, indicating it is denser than water. This means the liquid will provide more buoyant force compared to water, allowing the ice to float by displacing less volume than it would in water.
Understanding specific gravity helps us determine how substances interact when mixed or when objects are submerged, like ice in different liquids.

Water Displacement

Water displacement is a key principle in buoyancy and affects how objects like ice float in a liquid. When an object is placed in a fluid, it displaces a volume of that fluid equal to the volume or weight of the object submerged.
For floating objects, like the pieces of ice in the beakers, they displace water (or a liquid) equal to their weight. This means that a floating object displaces a certain volume of liquid and experiences an upward buoyant force. When ice melts, the melted water occupies a volume equal to the displaced volume when it was solid, hence in beaker A, the water level stays the same.

• Understanding this concept is crucial for predicting the behavior of sinking or floating objects.

Melting Ice

Melting ice is an interesting phenomenon in the context of water displacement and buoyancy. Ice, when it melts, transforms into liquid water. This process doesn't change the mass of the water but alters its volume because of the different densities of ice and liquid water.
In beaker A, where ice floats in water, upon melting, the ice turns into water, filling the space it occupied when it was solid. Hence, the water level remains unchanged.
Conversely, in beaker B, a denser liquid surrounds the ice. Upon melting, the volume of water produced by the ice is greater than the initial volume of displaced liquid. Therefore, the liquid level in beaker B increases.

Density of Water

Density is the measure of mass per unit volume, and water has a standard density of 1 g/cm³ or 1000 kg/m³ at 4°C. This property serves as the standard reference for specific gravity comparisons.
Ice, when frozen, is less dense than liquid water, which is why it floats. As ice melts, the density of the resulting water matches that of the surrounding water (1.0 in beaker A) but is less than the miscible liquid of specific gravity 1.2 in beaker B.

• It is important to note that the density of water and its changes in form greatly influence buoyancy and the resulting water levels in any vessel.

Understanding the density of water is foundational to grasping why objects float or sink and how their physical states affect fluid displacement.