A certain rain cloud at an altitude of `2.0 km` contains `3.6 xx 10^(7) kg` of water vapour. How long would it take a `2.0 kW` pump to raise the same amount of water from the Earth's surface to the cloud's position?

Options

A. `2 xx 10^(5) h`
B. `5 xx 10^(5) h`
C. `5 xx 10^(3) h`
D. `2 xx 10^(3) h`

Answer

B

Explanation

Neglecting any varition of gravity with altitude, the work required to lift a `3.60 xx10^(7) kg` load at constant speeds to an altitude of ` Deltay =2.0 km` is .
`W=DeltaPE_(g) =mg(Deltay)`
`=(3.6xx10^(7)kg) (10.0 m//s^(2)) (2.0xx10^(3) m)`
` =7.2 xx 10^(11) J`
The time required to do this work using a `P=2.0 kW`
`=2.0xx10^(3) J//s` pump
`Delta t=(W)/(P) =(7.2xx10^(11) J)/(2.0xx10^(3) J//s)=3.6xx10^(8) s`
`=(3.6xx10^(8) s) ((1h)/(3600 s))=5xx10^(5) h`.