A rain cloud contains 3.11 × 107 kg of water vapor.
The acceleration of gravity is 9.8 m/s2 .
How long would it take for a 1.8 kW pump to lift the same amount of water to an altitude of 20000 m?
Answer in units of years
Well, let's crunch some numbers and see if we can make this calculation rain with humor!
First, we need to find out how much work needs to be done to lift that 3.11 × 10^7 kg of water vapor to an altitude of 20000 m.
The work done is given by the formula: W = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
So, the work done would be: W = (3.11 × 10^7 kg)(9.8 m/s^2)(20000 m).
Now, we need to figure out how long it would take for a 1.8 kW pump to do this work.
To find the time, we can use this formula: time = work / power.
The power of the pump is 1.8 kW, which is equivalent to 1800 joules per second (since 1 W = 1 J/s).
Plugging in the values, we get: time = (3.11 × 10^7 kg)(9.8 m/s^2)(20000 m) / 1800 J/s.
Now, let's simplify things a bit.
3.11 × 10^7 kg times 9.8 m/s^2 is approximately 3.05 × 10^8 N (newtons).
Dividing that by 1800 J/s gives us 1.7 × 10^5 seconds.
And now, for the moment of truth...
To convert seconds to years, we need to divide by the number of seconds in a year, which is roughly 3.16 × 10^7 seconds (give or take a few cosmic chuckles).
So, the final answer is approximately 5.39 years (rounding to two decimal places).
In conclusion, it would take about 5.39 years for a 1.8 kW pump to lift the same amount of water to an altitude of 20000 m. But hey, who needs that pump when you've got a rain cloud ready to shower you with some wet humor? Stay hydrated, my friend!
To find the time it takes for a 1.8 kW pump to lift the same amount of water to an altitude of 20,000 m, we need to calculate the work done by the pump and then use it to determine the time.
The work done by the pump is given by the formula:
Work = Force x Distance
To calculate the force, we need to determine the mass of the water that needs to be lifted. We know the mass of the water vapor in the rain cloud, but we need to convert it to the mass of water. Since water vapor has a molar mass of 18 g/mol and the molar mass of water is 18 g/mol, we can assume that 1 mol of water vapor corresponds to 1 mol of water. Therefore, the mass of water is also 3.11 × 10^7 kg.
Now let's calculate the force:
Force = mass x gravitational acceleration
Force = (3.11 × 10^7 kg) x (9.8 m/s^2)
Next, we can calculate the work done:
Work = Force x Distance
Work = (Force) x (distance lifted)
Finally, we can determine the time using the power formula:
Power = Work / Time
Rearranging the formula to solve for time gives us:
Time = Work / Power
Substituting the values we have:
Time = (Work) / (Power)
Time = [(Force) x (distance lifted)] / (Power)
Plugging in the known values:
Time = [(3.11 × 10^7 kg) x (9.8 m/s^2) x (20,000 m)] / (1.8 kW)
Now we need to convert the power from kilowatts to watts:
1 kilowatt (kW) = 1000 watts (W)
1.8 kW = 1,800 W
Substituting the converted power value:
Time = [(3.11 × 10^7 kg) x (9.8 m/s^2) x (20,000 m)] / (1,800 W)
Finally, we calculate the time:
Time = (6036400000 kg*m^2/s^2) / (1800 W)
Time ≈ 3353555.56 seconds
To convert this to years, we divide the time in seconds by the number of seconds in a year:
1 year ≈ 31536000 seconds
Time (in years) = 3353555.56 s / 31536000 s/year
Time (in years) ≈ 0.1064 years
Therefore, it would take approximately 0.1064 years, or about 0.1 years, for a 1.8 kW pump to lift the same amount of water to an altitude of 20,000 m.