A bubble has a radius of 4 mm. Assuming that the bubble is a perfect sphere, what is the surface area of that bubble?
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It might help to define what the adjective of absolute means first. Absolute pressure means the actual force per unit area which the fluid exerts on the walls of its container. Absolute pressure it the P in the ideal gas law. Gauge pressure is pressure measured relative to the background pressure. If the pressure is equal to the background pressure, the gauge pressure is zero. If the pressure is greater than background, the pressure is a positive number. If the system is a partial vacuum, the gauge pressure is a negative number. There isn't really "the equation to use to find absolute pressure", you just need to keep these definitions in mind. ------------------------------- At the surface, the bubble has a standard atmosphere of absolute pressure. The atmosphere of pressure is a standard value of 101325 Pascals, unless otherwise indicated. Beneath the surface, the bubble has greater than an atmosphere of absolute pressure, due to being submerged a distance h. This problem is simple use of the ideal gas law. P1*V1 = n*R*T P2*V2 = n*R*T Because temperature and amount of gas are constant, n*R*T is a constant. Thus: P1*V1 = P2*V2 We desire to know P1, the pressure of the bubble at the depth prior to rising. Solve for P1: P1 = P2*V2/V1 Express each volume in terms of a sphere's radius: V1 = 4/3*Pi*R1^3 V2 = 4/3*Pi*R2^3 Thus: P1 = P2*R2^3/R1^3 We know that P2 is the atmospheric pressure, and we know the radii. Data: P2 := 101325 Pa; R1:=5 mm; R2:=7.4 mm; Result: P1 = 328475 Pascals I don't know why they want regular pascals, when kilopascals do it more justice: P1 = 328.5 kPa
Surface Area = 4 pi r^2
SA = 4 * pi * 4^2
SA = 64 pi which is approx 201.1 square millimeters
Surface area of sphere = 4πr^2 = 4π(4)^2 = 64π mm^2
Do you understand that?