8) The effect of surface tension is observable as bubbles, i.e., liquid in the s

Question

8) The effect of surface tension is observable as bubbles, i.e., liquid in the shape of a hollow sphere can minimize its surface area, and hence its free energy, by contracting. Were it not for the presence of a gas inside the bubble, it would contract to a spherical droplet of minimum surface area. However, as it contracts, the gas inside is compressed and an excess ressure exerts an outward force to counteract the contraction. At equilibrium, the inward force (4y/r, since there are two surfaces) exactly balances the pressure difference, and the excess pressure inside the bubble must be AP4y/r. Calculate the pressure inside a 1 mm (radius) bubble of methanol at 20°c. The surface tension of methanol at 20°C is y- 22.6 dyne/cm 22.6 x 10-3 N/m.

Explanation / Answer

The pressure inside the bubble = 90 N/m2

--calculations--

The pressure difference, Pi ? Po, between the inside and outside of a bubble is given by the Equation

Pi - Po = ?P = 4?/R

? (surface tension ) of methanol = 22.6 x 10-3 N/m

Radius of the bubble = 1 mm = 1 x 10-3 m

?P = 4 x 22.6 x 10-3 N/m / 1 x 10-3 m = 90 N/m2.

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