Find the gauge pressure in pascals in a soap bubble 0.04 m in diameter. The surface tension is 25.0 x 10^4 Pa.
hint:
Assume the soap bubble is free-floating in the air:
Pi-Po=4T/r
4r/g
4x30.0x10/2x10
1200/20
60N/M
To find the gauge pressure in a soap bubble, you can use the formula:
Gauge Pressure = 2 * Surface Tension / Radius
Step 1: Convert the diameter of the bubble to its radius.
Given diameter = 0.04 m
Radius = diameter / 2 = 0.04 m / 2 = 0.02 m
Step 2: Substitute the values into the formula.
Surface Tension = 25.0 x 10^4 Pa
Radius = 0.02 m
Gauge Pressure = 2 * 25.0 x 10^4 Pa / 0.02 m
Gauge Pressure = 2500 x 10^4 Pa = 2.5 x 10^7 Pa
Therefore, the gauge pressure in the soap bubble is 2.5 x 10^7 pascals.
To find the gauge pressure in a soap bubble, we need to use the formula for the excess pressure inside a bubble due to surface tension:
P = 4T/r
where P is the excess pressure, T is the surface tension, and r is the radius of the bubble.
First, we need to convert the diameter of the bubble to its radius:
r = diameter / 2 = 0.04 m / 2 = 0.02 m
Next, we substitute the given values into the formula:
P = 4 * 25.0 x 10^4 Pa / 0.02 m
Now let's calculate the pressure:
P = 100 x 10^4 Pa / 0.02 m
P = 5 x 10^6 Pa
Therefore, the gauge pressure inside the soap bubble is 5 x 10^6 Pa.