A rain cloud contains 2.66 X 10? kg of water vapor. How long would it take for a 2.00 kW pump to raise the same amount of water to the cloud's altitude, 2.00 km?

Answer 1

First, let's calculate the amount of work needed to raise the water vapor to the cloud's altitude.

Work = mgh

where:
m = mass of water vapor = 2.66 X 10^3 kg
g = acceleration due to gravity = 9.81 m/s^2
h = height = 2.00 km = 2000 m

Work = (2.66 X 10^3 kg) * (9.81 m/s^2) * (2000 m)
Work = 5.24 X 10^7 J

Next, let's calculate the time it would take for a 2.00 kW pump to do this amount of work.

Power = Work / time

time = Work / Power
time = (5.24 X 10^7 J) / (2.00 kW)
time = (5.24 X 10^7 J) / (2.00 X 10^3 W)
time = 2.62 X 10^4 seconds

Therefore, it would take approximately 26,200 seconds or 7.28 hours for a 2.00 kW pump to raise the same amount of water to the cloud's altitude.