From La Place's law, we know that, at any given surface tension, it is the ___ alveoli which require greater opening pressures, and therefore these have ____ tendency to collapse.

Question

BlackTom AI · Accepted Answer

Laplace's law for a spherical bubble: P = 2T / r, where P is the inward pressure required to oppose surface tension T for a sphere of radius r.

1) Relevant concepts
- Laplace's law quantifies how surface tension and radius determine the pressure required to keep a spherical surface open.
- In the lung, alveoli are approximated as small spheres; surface tension tends to collapse them unless balanced by internal pressure and surfactant.
- With the same surface tension, pressure is inversely proportional to radius.

2) Step-by-step reasoning
- Start from P = 2T / r. Hold T constant (same surface tension across alveoli).
- This shows P ∝ 1/r: as r decreases, P increases.
- Therefore, a smaller alveolus (smaller r) requires a larger internal pressure to remain open than a larger alveolus.

3) Numerical illustration (intermediate steps)
- Let T = 0.05 N/m. For r1 = 0.05 m: P1 = 2×0.05 / 0.05 = 2 (arbitrary units).
- For r2 = 0.02 m: P2 = 2×0.05 / 0.02 = 5.
- P2 > P1, so the smaller alveolus requires greater opening pressure.

4) Why the correct answer is correct
- Since smaller alveoli require a higher inward pressure to balance the same surface tension, they are more prone to emptying into larger alveoli (and to collapse, i.e., atelectasis) unless surfactant reduces T in a radius-dependent manner. Thus “Smaller, greater” correctly captures that smaller alveoli need greater opening pressures and have greater tendency to collapse.

5) Why the other choices are incorrect
- “Larger, less”: larger alveoli require less pressure (true about pressure) but the pairing implies larger alveoli both require greater opening pressures and have less tendency to collapse — the wording is inconsistent with Laplace’s law.
- “Larger, greater”: contradicts P ∝ 1/r; larger r gives smaller P, not greater.
- “Smaller, less”: contradicts the law because smaller radius increases required pressure, not decreases it.

Conclusion: By applying Laplace’s law (P = 2T/r), smaller alveoli require greater opening pressures and therefore have greater tendency to collapse, confirming the correct answer: Smaller, greater.

From La Place's law, we know that, at any given surface tension, it is the _ alveoli which require greater opening pressures, and therefore these have __ tendency to collapse.单项选择题

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From La Place's law, we know that, at any given surface tension, it is the ___ alveoli which require greater opening pressures, and therefore these have ____ tendency to collapse.单项选择题