## Atmospheric conditions near the Gulf of Mexico are such that a cloud at an altitude of 1.90 km contains 3.20 ✕ 107 kg of water vapor. How lo

Question

Atmospheric conditions near the Gulf of Mexico are such that a cloud at an altitude of 1.90 km contains 3.20 ✕ 107 kg of water vapor. How long (in years) would it take for a 2.21 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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5 months 2021-08-18T02:04:39+00:00 1 Answers 54 views 0

t = 8.55 years

Explanation:

The formula for power is given as:

Power = Work/Time

but, the work here is equal to the increase in potential energy of the water. Therefore,

Power = P.E/Time

P = mgh/t

t = mgh/P

where,

t = time required = ?

P = Power of pump = 2.21 KW = 2210 W

m = mass of water = 3.2 x 10⁷ kg

h = height = 1.9 km = 1900 m

g = 9.8 m/s²

Therefore,

t = (3.2 x 10⁷ kg)(9.8 m/s²)(1900 m)/(2210 W)

t = (2.69 x 10⁸ s)(1 h/3600 s)(1 day/24 h)(1 year/365 days)

t = 8.55 years