To calculate the amount of work needed to raise the water to the cloud's altitude, we first need to convert the mass of the water vapor to volume.
Density of water is approximately 1000 kg/m^3.
Volume of water vapor = Mass / Density
Volume of water vapor = 2.66 X 10^7 kg / 1000 kg/m^3
Volume of water vapor = 2.66 X 10^4 m^3
Next, we need to calculate the height the pump must raise the water to reach the cloud's altitude.
Height = 2.00 km = 2.00 X 10^3 m
Now, we can calculate the work done by the pump using the formula:
Work = Force x Distance
Force = Mass x Acceleration due to gravity = 2.66 X 10^7 kg x 9.8 m/s^2
= 2.6108 X 10^8 N
Work = 2.6108 X 10^8 N x 2.00 X 10^3 m
Work = 5.2216 X 10^11 J
Finally, we can calculate the time it would take for the 2.00 kW pump to do this work:
Power = Work / Time
Time = Work / Power
Time = 5.2216 X 10^11 J / 2.00 X 10^3 W
Time = 2.6108 X 10^5 seconds
Therefore, it would take approximately 2.61 X 10^5 seconds for a 2.00 kW pump to raise the same amount of water to the cloud's altitude.
A rain cloud contains 2.66 X 10^7 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?
1 answer