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Chapter 7: Problem 989

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

Expert verified
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

01

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 \(0.02 \mathrm{~m}^{2}\).
02

Apply the formula for surface energy

To find the surface energy (E), we use the formula: Surface Energy (E) = Surface Tension (T) × Area (A)
03

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)
04

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
05

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) \(2 \times 10^{-1} \mathrm{~J}\).

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