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Tough Science Question... Higher or Lower?

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wnwood88 | 02:32 Thu 21st Feb 2008 | Science
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On her approach to Denver, Amelia can see a heavy cloak of smog shrouding the city. Rather than passing around the noxious atmosphere, she resolves to go over it. She is flying at an altitude of 10,000' above sea level (only about 5,000' above ground level) and decides to ascend until the outside temperature declines from its current level of 60 degrees Fahrenheit to a target level of 40 degrees Fahrenheit. As Amelia ascends, she finds that the lapse rate is normal and that she is going to be leaving the smog well below her wings. When she finally levels off with the outside temperature registering at 40 degrees, is she flying higher than or lower than the highest peaks in the Colorado Rockies? They are, after all, rather near.


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The standard lapse rate in Fahrenheit is 3.5 degrees F per 1,000 feet of altitude. So, if she's losing 20 degrees F (60 to 40) she has climbed 3.5 X 20 or 7,000 feet. Her altitude is now 17,000 feet MSL (above mean sea level). The highest mountain in Colorado is Mount Elbert, at 14,433 feet MSL... so, she's good to go...
Actually, I erred (can you believe it?) The 20 degree difference should be divided by the lapse rate of 3.5 degrees yelding 5.7 or 5,700 feet. Still, added to the 10,000 feet starting altitude, our intrepid Amelia would be at 15, 700 feet MSL, still clearing Mt. Elbert by more than 1,000 feet...

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