On a nice day when the temperature outside is 20 °C, you take the elevator to the top of the Sears Tower in Chicago, which is 440 m tall.
(a) How much less is the air pressure at the top than the air pressure at the bottom? Express your answer both in pascals and atm.
(b) How many pascals does the pressure decrease for every meter of altitude?
(c) If the pressure gradient- the pressure decrease per meter of altitude-were uniform, at what altitude would the atmospheric pressure reach zero?
(d) Atmospheric pressure does not decrease with a uniform gradient since the density of air decreases as you go up. Which is true: the pressure reaches zero at a lower altitude than your answer to (c), or the pressure is nonzero at that altitude and the atmosphere extends to a higher altitude? Explain.