Final answer:
The gauge pressure of a soap bubble with a diameter of 0.100 m in millimeters of mercury is calculated using the surface tension of soapy water and its radius, ultimately yielding a pressure of 0.50 mm Hg. Option b is the correct answer.
Step-by-step explanation:
The gauge pressure in millimeters of mercury inside a soap bubble can be calculated using the formula that relates pressure, surface tension, and radius of the bubble. For a soap bubble with a given diameter, we use half of that as the radius in our calculations. Utilizing the characteristics of surface tension for soapy water, we can then translate the pressure value from pascals to millimeters of mercury (mm Hg).
To solve the problem, the following relationship is used for the pressure P inside a spherical bubble:
P = 4T/r, where T is the surface tension of soapy water and r is the radius of the bubble.
Given that soapy water has a surface tension of approximately 0.037 N/m (value could be found in a standard table of surface tension values), and converting the diameter of the bubble into radius (0.100 m diameter translates to a 0.050 m radius), the pressure in pascals can be calculated. Then, to find the gauge pressure in millimeters of mercury, we use the conversion factor 1 atm = 101,325 Pa = 760 mm Hg.
Following these steps and calculations, we can conclude that the correct answer is (b) 0.50 mm Hg.