A spherical soap bubble with a surface-tension of 0.005lbf/ft is expanded from a diameter of 0.5 in to 3.0 in. How much work, in Btu, is required to expand this bubble

1.23E-6 Btu

Explanation:

Given

Surface Tension, s = 0.005lbf/ft

First we'll calculate the initial and final area (A1 and A2) of the Bubble.

Given that D1 = 0.5in and D2 = 3in

Convert units of D1 and D2 to feet

D1 = 0.5ft/12 = 0.041667 ft

D2 = 3ft/12 = 0.25 ft

Work done = s(A2 - A1)

Work = s(πD2² - πD1²)

Work = sπ(D2² - D1²)

Work = 0.005π(0.25² - 0.041667²)

Work = 0.005 π * 0.060763861111

Work = 0.000954860674601 lbft

Convert to BTU

Work = 0.000954860674601BTU ÷ 778

Work = 0.0000012273273452460

Work = 1.23E-6 BTU

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