(a) As dry air moves upward, it expands and cools. If the ground temperature is
ID: 2892680 • Letter: #
Question
(a) As dry air moves upward, it expands and cools. If the ground temperature is 35 degree C and the temperature at a height of 1 km is 20 degree C, express the temperature T (in degree C) as a function of the height h (in kilometers), assuming that a linear model is appropriate. (b) Draw the graph of the function in part (a). What does the slope represent? (c) What is the temperature at a height of 2.5 km? (a) Because we are assuming that T is a linear function of h, we can write T = mh + b. We are given that T = 35 when h = 0, so 35 = m middot + b In other words, the y - intercept is b = We are also given that T = 20 when h = 1, so 20 = m + The slope of the line is therefore m = 20 - = and the required linear function is T = h + (b) The graph is sketched in the figure. The slope is m = degree C/km, and this represents the rate of change of I height with respect to (c) At a height of h = 2.5 km, the temperature is T = 2.5 + 35 = degree C.Explanation / Answer
a) 35 =m*0+b
=b
in other words the Y nintercept is b=35
we are also given that T=20 when h=1, so
20=m*1+35
the slope of the...m=20-35=-15 and the required linear function is
T=-15*h+35
b) the slope is m=-15 oC/Km and this represent the ratre of change of tempearture with respect to height.
c) at a height of 2.5 KN , the temperature is
T=-15*2.5+35=-2.5oC
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