   Chapter 2, Problem 12RQ

Chapter
Section
Textbook Problem

According to Laplace’s law, if a bubble with a radius of 4 cm and a distending pressure of 10 cm H2O is reduced to a radius of 2 cm, the new distending pressure of the bubble will beA. 5 cm H2O.B. 10 cm H2O.C. 15 cm H2O.D. 20 cm H2O.

Summary Introduction

Introduction:

The cohesive force that occurs at the liquid-gas interface through which the liquid molecules are strongly attracted to the molecules in the bulk of the liquid is termed as surface tension. Laplace’s law describes that the distending pressure of a liquid sphere is directly proportional to the surface tension of the liquid and inversely proportional to the radius of the sphere. This law is also applied to the alveoli of lungs because the alveoli are also in contact with each other and there also exists a surface area, which is the intra-alveolar surface area. The equation of Laplace’s law is:

Pressure, P=2STr

Where ST is the surface tension measured in dynes per centimeters and r is the radius of the liquid sphere in centimeters.

Explanation

Justification/ Explanation for the correct answer:

Option (d) states that the new distending pressure of the bubble would be 20 cm H2O when the radius is changed from 4 cm to 2 cm, which is the correct option. The distending pressure is determined by the Laplace’s law, according to which the pressure is inversely proportional to the radius of the bubble.

P (old pressure)=2STr (old radius)=2ST4 cm

P' (new pressure)=2STr'(new radius)P'=2STr' =2ST2cm =4×2ST4×2cm

=42(2ST4cm

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