Problem 1064 - JEE Physics

Question

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

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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.

Step 3: 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.

Step 4: 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).

Key Concepts

Density of Water

Water is a fascinating substance, and one of its most intriguing properties is its density behavior. Density refers to the amount of mass per unit volume of a substance. For most materials, as temperature increases, their density decreases because they expand. However, water is special because it reaches its maximum density at exactly \(4^{\circ} \mathrm{C}\). This means that at this temperature, water is at its most compact form.

Once you either heat or cool water beyond this temperature, it begins to expand. With this knowledge, if you have a container completely filled with water at \(4^{\circ} \mathrm{C}\), any change in temperature will make the water less dense and potentially cause overflow because it begins to occupy more space.

This behavior is unique to water due to the structure and bonding of water molecules. Always remember this peculiar trait when considering water's behavior with temperature changes.

Temperature Effects on Water Volume

The volume of water is highly dependent on its temperature. At \(4^{\circ} \mathrm{C}\), water reaches its smallest volume due to its highest density. But as you change the temperature, the volume starts to increase. Here's how it works:

• When heated beyond \(4^{\circ} \mathrm{C}\), water molecules move faster and spread out, leading to an increase in volume.
• When cooled below \(4^{\circ} \mathrm{C}\), water also expands. It's counterintuitive, but due to the rearrangement of hydrogen bonds as it cools further, the volume increases too.

This behavior means that water can overflow from a filled beaker when heated or cooled past this temperature due to volume expansion. In practical terms, understanding this property is crucial in designing systems that use water, such as heating systems or coolant designs, where temperature fluctuations might lead to pressure changes or leaks.

Anomalous Expansion of Water

Water is renowned for its anomalous expansion. Anomalous means that it behaves differently from most other substances. While most substances contract as they cool, water expands as it cools below \(4^{\circ} \mathrm{C}\). This unusual behavior occurs because of the formation of a crystalline structure that takes up more space.

As water temperatures drop from \(4^{\circ} \mathrm{C}\) to \(0^{\circ} \mathrm{C}\), it expands to form ice. Ice is less dense than liquid water, which is why it floats. This property of water is vital for aquatic life, as it provides insulation to bodies of water in cold climates, preventing them from freezing solid.

Remember that this anomaly is due entirely to the hydrogen bonds between water molecules and their specific arrangement as temperature lowers. Understanding this concept is essential, especially in scientific applications, where predicting water behavior at varying temperatures is necessary.