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Chapter 7: Problem 1064

A beaker is completely filled with water at \(4^{\circ} \mathrm{C}\) It will overflow if (A) Heated above \(4^{\circ} \mathrm{C}\) (B) Cooled below \(4^{\circ} \mathrm{C}\) (C) Both heated and cooled above and below \(4^{\circ} \mathrm{C}\) respectively (D) None of these

Short Answer

Expert verified
The correct answer is (C). A beaker filled with water at \(4^{\circ} \mathrm{C}\) will overflow if both heated and cooled above and below \(4^{\circ} \mathrm{C}\), respectively, because the water's density is highest at \(4^{\circ} \mathrm{C}\), and it will expand when heated or cooled.

Step by step solution

01

Understanding Density and Temperature Relationship of Water

Water's density depends on its temperature. As temperature increases, the density of most substances decreases. However, water has an unusual property: its density is highest at \(4^{\circ} \mathrm{C}\). This means that water is most "compressed" at this temperature, and as temperature moves either higher or lower, the water expands, occupying a larger volume.
02

Determine the Overflow Condition for Heating

If the water is heated above \(4^{\circ} \mathrm{C}\), its density will decrease, causing it to expand. Since the beaker is already completely filled, this will result in an overflow. This means that option (A) is true.
03

Determine the Overflow Condition for Cooling

If the water is cooled below \(4^{\circ} \mathrm{C}\), its density will also decrease, causing it to expand. As in the heating scenario, since the beaker is already completely filled, this expansion will cause an overflow. This means that option (B) is also true.
04

Identify the Correct Option

Since both options (A) and (B) are correct, we can answer the question with option (C), which states that the beaker will overflow if both heated and cooled above and below \(4^{\circ} \mathrm{C}\), respectively. Therefore, the correct answer is (C).

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