$(30$ pts$)$ A soap bubble of diameter $24\mathrm{.}50$ mm is filled with air. The absolute pressure outside the bubble is $100\mathrm{.}5$ kPa $.$ The gage pressure inside the bubble is $15\mathrm{.}90$ Pa $.$ The temperature both inside and outside of the bubble is $20\mathrm{.}00C.$ Give all answers to $4$ significant digits.

$($a$)$ Calculate the absolute pressure in kPa inside the bubble. Compare to the pressure outside the bubble and discuss.

$($b$)$ Calculate the density of the air inside and outside the bubble. Compare and discuss.

$($c$)$ Calculate the surface tension of the soapy water and compare to that of pure water at the same temperature. Discuss.