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19 December, 12:46

Atmospheric conditions near a mountain range are such that a cloud at an altitude of 2.00 km contains 3.20 ✕ 10^7 kg of water vapor. How long (in years) would it take for a 2.96 kW pump to raise this amount of water (at a constant speed) from Earth's surface to the altitude of the cloud?

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  1. 19 December, 16:39
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    time required is 6.72 years

    Explanation:

    Given data

    mass m = 3.20 ✕ 10^7 kg

    height h = 2.00 km = 2 * 10^3 m

    power p = 2.96 kW = 2.96 * 10^3 J/s

    to find out

    time period

    solution

    we know work is mass * gravity force * height

    and power is work / time

    so we say that power = mass gravity force * height / time

    now put all value and find time period

    power = mass * gravity force * height / time

    2.96 * 10^3 = 3.20 ✕ 10^7 * 9.81 * 2 * 10^3 / time

    time = 62.784 * 10^10 / 2.96 * 10^3

    time = 21.21081081 * 10^7 sec

    time = 58.91891892 * 10^3 hours

    time = 6.72 years

    so time required is 6.72 years
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