Question

If a soap bubble expands, the pressure inside the bubble:

• A. decreases
• B. decreases
• C. remains the same
• D. In equal to the atmospheric pressure

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
A soap bubble has two free surfaces. The pressure inside a soap bubble is always greater than the external atmospheric pressure due to surface tension.
Key Formula or Approach:
The excess pressure (\(P_{ex}\)) inside a soap bubble of radius \(R\) and surface tension \(T\) is:
\[ P_{in} - P_{out} = \frac{4T}{R} \]
So, the total pressure inside is:
\[ P_{in} = P_{atm} + \frac{4T}{R} \]
Step 2: Detailed Explanation:
1. When the soap bubble expands, its radius \(R\) increases.
2. From the formula for excess pressure, we see that \(P_{ex}\) is inversely proportional to the radius (\(P_{ex} \propto \frac{1}{R}\)).
3. As \(R\) increases, the term \(\frac{4T}{R}\) becomes smaller.
4. Since \(P_{atm}\) and \(T\) (assuming constant temperature) remain constant, the overall value of \(P_{in}\) decreases.
Therefore, as a bubble gets larger, the air pressure inside it decreases.
Step 3: Final Answer:
The pressure inside the bubble decreases as it expands.