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Calculate the gauge pressures inside 2.00 -cm-radius bubbles of water, alcohol, and soapy water. Which liquid forms the most stable bubbles, neglecting any effects of evaporation?

(i) $P_{\text {water }}=14.6 \mathrm{Pa}$(ii) $P_{\text {alcohol }}=4.5 \mathrm{Pa}$(iii) $P_{\text {soap }}=7.40 \mathrm{Pa}$Alcohol forms the most stable bubbles.

Physics 101 Mechanics

Chapter 11

Fluid Statics

Fluid Mechanics

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Sheffield

McMaster University

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so the pressure inside the water bubble would be equaling four times the surface tension of water divided by the radius. And so this is gonna be equaling Tau four times the surface tension of 0.7 to 8 newtons per meter. And this would be divided bye the radius of point 02 meters. And so the pressure would be 14.6 newton per meter squared. Now this would be for water for alcohol. We're doing the exact same process. Except now we're using the surface tension for alcohol. So this would be equaling to four times the surface tension of alcohol. We know to be point 0223 Newtons per meter and this this would be divided by again point 02 meters. And this is equaling 4.46 times 10 to by the 4.46 rather Newtons per square meter and then the pressure force for soap, water or a soapy water. We could say so. This would be equaling four times the surface tension of soapy water, so 40.0 37 zero Newtons per meter and then divided by the same exact radius of 00.2 meters. This is equaling 7.40 Newton's per square meter. And the last question is asking which liquid forms the most stable bubbles, neglecting any effects from the operation. And because we can say because the pressure of the alcohol bubble is closest to atmospheric pressure, we can say the alcohol bubble is the most stable bubble. Now we're not taking account into. We're not taking into account rather evaporation effects, and that would actually prove if we were taking into account, of course, we'd have to do more calculations. But also, we know that the boiling point, or rather, yeah, the boiling point of, uh, alcohol is very low. So, in fact, it may not prove to be the most stable bubble. But, um, when not taking into account evaporation effects again, the pressure of the alcohol is closer is closest to atmospheric pressure, and that is why it is the most stable bubble that is the end of the solution. Thank you for watching

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