Question

The surface tension of a liquid is \(5 \mathrm{~N} / \mathrm{m}\). If a thin film of the area \(0.02 \mathrm{~m}^{2}\) is formed on a loop, then its surface energy will be (A) \(5 \times 10^{-2} \mathrm{~J}\) (B) \(2.5 \times 10^{-2} \mathrm{~J}\) (C) \(2 \times 10^{-1} \mathrm{~J}\) (D) \(5 \times 10^{-1} \mathrm{~J}\)

Short answer

The surface energy (E) can be found using the formula: E = Surface Tension (T) × Area (A). Given the surface tension (T) as \(5 \mathrm{~N} / \mathrm{m}\) and area (A) as \(0.02 \mathrm{~m}^{2}\), we can calculate the surface energy by substituting these values: E = (5 N/m) × (0.02 m²) = 0.1 J. Comparing the calculated surface energy with the answer choices, the correct answer is (C) \(2 \times 10^{-1} \mathrm{~J}\).

Step-by-step solution

Identify the given values

We are given the surface tension (T) which is \(5 \mathrm{~N} / \mathrm{m}\) and area (A) of the thin film as \(0.02 \mathrm{~m}^{2}\).

Apply the formula for surface energy

To find the surface energy (E), we use the formula: Surface Energy (E) = Surface Tension (T) × Area (A)

Plug the values into the formula

Now substitute the given values of surface tension and area into the formula: E = (5 N/m) × (0.02 m²)

Calculate the surface energy

Multiply the given values of surface tension and area to obtain the surface energy: E = 5 × 0.02 J E = 0.1 J

Match the answer with the answer choices

Now compare the calculated surface energy with the given answer choices. Our calculated surface energy is 0.1 J, which matches the answer (C). So, the correct answer is (C) \(2 \times 10^{-1} \mathrm{~J}\).

Key concepts

Surface Energy

Surface energy is a fascinating topic in physics that relates to the idea of how much energy is needed to increase the surface area of a liquid. Imagine stretching a rubber band; it requires some energy, right? Similarly, when you increase the surface of a liquid, energy is required. This is because molecules on the surface experience different forces compared to those inside. The energy needed to expand the surface by one unit area is called surface energy. Understanding surface energy helps us grasp why droplets form or why some liquids spread while others bead up. It's a crucial concept in understanding various physical phenomena and plays a significant role in several real-world applications.

Physics Problem Solving

Whether you're a beginner or a seasoned physicist, solving physics problems involves a structured approach. The first step is always to identify the given values. For our original problem, these were the surface tension and the area of the liquid film. Next, you determine which formulas are relevant to the problem. In this case, we used the formula for surface energy. Any physics problem boils down to this sequence: identifying details, applying the right formula, and performing calculations carefully. Approaching problems systematically helps build critical thinking skills, making complex topics manageable. It's like following a recipe—each step gets you closer to the solution.

Formula Application

Applying formulas in physics isn't just about plugging numbers into equations; it's about understanding what those numbers mean and how they relate to each other. In our case, we used the formula:\[E = T \times A\]Where \(E\) is the surface energy, \(T\) the surface tension, and \(A\) the area. This formula tells us that the surface energy depends directly on both the tension of the surface and the size of the area. By substituting known values into this formula, we can calculate unknowns. Effective formula application requires knowing your variables and proper substitution, ensuring accurate and reliable results.

Liquid Film

The concept of a liquid film involves a thin layer of liquid bound by surfaces. Think of it as a soap bubble or an oil spill on water. These films are fascinating because they behave differently than bulk liquids. A key characteristic of liquid films is the surface tension acting on them, which influences their shape and stability. The surface creates a force that aims to minimize tension, thereby reducing the surface area. This is why bubbles tend to be round—they minimize surface tension in a smaller area. This tendency to minimize surface tension is what gives liquid films their unique properties, making them essential in a range of sciences, from materials to biology.