13.3 A water bubble has radius 1 mm in air. Atmospheric pressure is 101.3 kPa an

Question

13.3 A water bubble has radius 1 mm in air. Atmospheric pressure is 101.3 kPa and the surface tension of water at room temperature is 0.073 N m^-1. (a) What is the gauge pressure inside the bubble? (b) If atmospheric pressure had been 101.2 kPa and the absolute internal pressure of the bubble was the same as in part (a), what would the radius of the bubble have been? (c) If the surface tension of the water was lowered to 0.037 N m (due to the addition of a surfactant for example), what would the radius of the bubble in part (b) be?

Explanation / Answer

(a) From Laplace pressure.

spherical shape is given (delta P) = 2 * (surface tension) / R

delta P = 2 * 0.073 / (1.0 * 10-3 m )

= 146 N.m-2 = 146 Pa

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(b) The absolute internal pressure in the bubble

P = Pa + delta P = 101,300 Pa - 146 Pa = 101,446 Pa

gauge pressure delta P = 101,446 Pa - 101,200 Pa = 246 Pa

R = 2 (surface tension) / delta P = 2 * 0.073 / 246

= 0.593 mm

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(c) R = 2 (surface tension) / delta P

= 2 * 0.037 / 246

= 0.30 mm

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