Question 837196: As dry air moves upward, it expands and in so doing cools at a rate of about 1°C for each 100-meter rise, up to about 42 km.
(a) If the ground temperature is 20°C, write a formula for the temperature at height h.
(b) What range of temperatures can be expected if a plane takes off an reaches a maximum height of 5 km?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe the formula will be:
T = G - H/100
T is temperature in centigrade degrees.
G is the temperature in centigrade degrees at ground level.
H is the height above ground level measured in meters.
assuming the temperature at ground level is 20 degrees centigrade, then G = 20.
the formula then becomes:
T = 20 - H/100.
at ground level, H = 0 and the formula becomes 20 - 0/100 = 20 degrees centigrade.
at 100 meters, H = 100 and the formula becomes 20 - 100/100 = 20 - 1 = 19 degrees centigrade.
at 200 meters, H = 200 and the formula becomes 20 - 200/100 = 20 - 2 = 18 degrees centigrade.
as can be seen, every additional 100 meters above ground level, the temperature drops 1 degree centigrade.
at 42 km above ground level, H = 42000 and the formula becomes 20 - 42000 / 100 = 20 - 420 = -400 degrees centigrade.
at 5 km above ground level, H = 5000 and the formula becomes 20 - 50 = -30 degrees centigrade.
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