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Chapter 7: Problem 1035

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

Expert verified
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

01

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.
02

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.
03

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.

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