latex/problems/Serway_and_Jewett_8/problem08.28.tex

   1 \begin{problem*}{8.28}
   2 A certain rain cloud at an altitude of $1.75\U{km}$ contains
   3 $3.20\E{7}\U{kg}$ of water vapor.  How long would it take a
   4 $2.70\U{kW}$ pump to raise the same amount of water from the Earth's
   5 surface to the cloud's position?
   6 \end{problem*}
   7
   8 \begin{solution}
   9 The gravitational potential energy of the cloud is
  10 \begin{equation}
  11   U_g = mgh = 3.20\E{7}\U{kg}\cdot9.80\U{m/s$^2$}\cdot1.75\U{km}
  12     = 549\U{GJ}
  13 \end{equation}
  14
  15 The pump would take
  16 \begin{align}
  17   P &= \deriv{t}{E} \\
  18   \Delta t &= \frac{E}{P} = \frac{549\U{GJ}}{2.70\U{kW}}
  19     = \ans{203\U{Ms} = 6.44\U{years}}
  20 \end{align}
  21 to raise the water.
  22 \end{solution}