Problem 63 - Master Resource Book in JEE Main Physics

Question

At which of the following temperatures, the value of surface tension of water is minimum? (a) \(4^{\circ} \mathrm{C}\) (b) \(25^{\circ} \mathrm{C}\) (c) \(50^{\circ} \mathrm{C}\) (d) \(75^{\circ} \mathrm{C}\)

Step-by-Step Solution

Answer

The surface tension of water is minimum at 75°C (option d).

Step 1: Understanding Surface Tension and Temperature

Surface tension is a physical property of liquids that causes them to behave like an elastic sheet. The temperature of a liquid influences its surface tension. As temperature increases, surface tension typically decreases because the added heat increases the kinetic energy of the molecules, causing them to become less tightly bound at the surface.

Step 2: Identifying the Relationship

The correct relationship between temperature and surface tension for water is that surface tension decreases as temperature increases. Therefore, we need to identify the highest temperature among the provided options, as that will correspond to the lowest surface tension value.

Step 3: Analyzing the Given Temperatures

The temperatures provided in the options are: - (a) 4°C - (b) 25°C - (c) 50°C - (d) 75°C Comparing these, the highest temperature is 75°C.

Step 4: Conclusion and Answer

Since surface tension decreases with increasing temperature, the surface tension of water is minimum at the highest temperature provided. Therefore, the answer is when the temperature is 75°C.

Key Concepts

Temperature Dependence of Surface Tension

Surface tension is an essential property of liquids that emerges from intermolecular forces at the liquid's surface. It makes the liquid act as if it were enclosed in an elastic membrane. The temperature dependence of surface tension is particularly significant because it helps explain how molecular behavior changes with temperature.

As the temperature of a liquid increases, the molecules within the liquid gain kinetic energy. This increase in energy causes the molecules to move more energetically. As a result, the cohesive forces that hold molecules together become weaker, leading to a decrease in surface tension.

• Higher temperature = Greater kinetic energy
• Greater molecule movement = Weaker intermolecular forces
• Weaker forces = Lower surface tension

Therefore, when comparing the surface tension at different temperatures, the lowest surface tension will be at the highest temperature.

Properties of Liquids

Liquids have unique properties that distinguish them from solids and gases. Their characteristics are largely a result of the balance between kinetic energy and intermolecular forces. Surface tension is just one of several intriguing properties.

Some important properties of liquids include:

• Viscosity: Resistance to flow which decreases with increasing temperature.
• Density: Usually decreases as temperature increases.
• Surface Tension: The elastic tendency at the surface of a liquid, dependent on temperature.

These properties are interconnected through the behavior of molecules in a liquid. As temperature changes, so do these properties, affecting how liquids behave in different environments and applications.

Kinetic Energy and Molecular Movement

Kinetic energy plays a crucial role in how molecules behave in a liquid. It is the energy of motion, and for molecules, it's all about how fast and energetically they move.

When a liquid is heated, the molecules absorb thermal energy, converting it into kinetic energy. This change increases the speed at which the molecules move. As kinetic energy rises:

• Molecules move more vigorously.
• Intermolecular forces weaken because molecules collide more often and move farther apart.
• The result is a decrease in properties like surface tension.

Understanding the link between kinetic energy and molecular movement is key to comprehending why temperature affects the physical properties of liquids so significantly.