Final answer:
The gauge pressure inside a soap bubble can be calculated using the equation P = AY, where P is the pressure, A is the area of the bubble, and Y is the surface tension. Given the diameter of the bubble and the surface tension, we can calculate the pressure inside the bubble. The pressure inside the soap bubble is 11.64 mm Hg.
Step-by-step explanation:
The gauge pressure inside a soap bubble can be calculated using the equation P = AY, where P is the pressure, A is the area of the bubble, and Y is the surface tension. Since the bubble is spherical, the area can be calculated using the formula A = 4πr^2, where r is the radius of the bubble. Given that the soap bubble has a diameter of 10 cm, the radius would be 5 cm. Plugging in the values, we have A = 4π(5 cm)^2 = 100π cm^2. The surface tension is given as 0.0370 N/m. Now, we can calculate the pressure inside the bubble using the formula P = AY.
P = 100π (0.0370 N/m) = 3.70π N/m = 11.64 N/m
To convert this pressure to millimeters of mercury (mm Hg), we use the conversion factor 1 N/m = 1 mm Hg. Therefore, the gauge pressure inside the soap bubble is 11.64 mm Hg.