Question

A rain cloud contains 5.32 × 107 kg of water vapor. The acceleration of gravity is 9.81 m/s 2 . How long would it take for a 2.07 kW pump to raise the same amount of water to the cloud’s altitude of 2.61 km? Answer in units of s.

Answer 1

To calculate the time required for a 2.07 kW pump to raise 5.32 × 10⁷ kg of water to a cloud at 2.61 km, we calculate the work needed and divide it by the power of the pump. The work is the product of mass, gravity, and height, and the time is the obtained work divided by the power output of the pump.

Step-by-step explanation:

The student asked how long it would take for a 2.07 kW pump to raise 5.32 × 107 kg of water vapor to the cloud's altitude of 2.61 km, considering gravity's acceleration of 9.81 m/s2.

To solve this problem, we must first find the total amount of work needed to raise the water, then calculate how long it would take for the pump to do this work.

Work can be calculated using the formula Work (W) = mass (m) × gravity (g) × height (h), which in this case is W = 5.32 × 107 kg × 9.81 m/s2 × 2.61 × 103 m.

Calculating this gives us the total work required to lift the water to the cloud. Next, since power (P) is the rate at which work is done, we use the formula Time (t) = Work / Power to find out how long it would take for the 2.07 kW pump to do this work.

Here, we must remember to convert kilowatts to watts by multiplying by 1,000.

Plugging in the values, we find that the pump would take a considerable amount of time to lift the water to the cloud's altitude, demonstrating the significant energy represented by a cloud's water content.

Answer 2

20.85 years

Step-by-step explanation:

2.61 km = 2610 m

2.07 kW = 2070 W

First we need to calculate the potential energy required to take m =
`5.32 * 10^7` kg of rain cloud to an altitude of 2610 m is

`E = mgh = 5.32 * 10^7 * 9.81 * 2610 = 1.4*10^(12)J`

With a P = 2070 W power pump, this can be done within a time frame of

`t = E/P = (1.4*10^(12))/(2070) = 658037739 s`

or 658037739/(60*60) = 182788 hours or 182788 / 24 = 7616 days or 7616 / 365.25 = 20.85 years