What power 2

What power has a pump output to move 4853 hl of water to a height of 31 m for 8 hours? Comparing the power generated by the pump vs. the power generated by the motor, which is more efficient? Which pump or motor generates more pollution if, for every watt of power, 320 ml of CO2 is released into the atmosphere?

Correct answer:

P =  5124.5 W

Step-by-step explanation:

$$\begin{gathered} V=4853\text{hl}\to {\text{m}}^3=4853:10{\text{m}}^3=485.3{\text{m}}^3 \\ h=31\text{m} \\ t=8\text{h}\to \text{s}=8\cdot 3600\text{s}=28800\text{s} \\ g=9.81{\text{m/s}}^2 \\ \rho =1000{\text{kg/m}}^3 \\ m=\rho \cdot V=1000\cdot \frac{4853}{10}=\frac{1000\cdot 4853}{10}=\frac{4853000}{10}=485300\text{kg} \\ W=m\cdot g\cdot h=485300\cdot 9.81\cdot 31=147584583\text{J} \\ P=\frac{W}{t}=\frac{147584583}{28800}=5124.5\text{W} \end{gathered}$$

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