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27 October, 02:42

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

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  1. 27 October, 05:33
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    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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