Dry air is moving upward. If the ground temperature is 200 and the temperature at a height of 1km is 100 C, express the temperature T in 0C 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 2km?

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Solution

a) Because we are assuming that T is a linear function of h, we can write

T = mh + b

We are given that T = 20 when h = 0, so

20 = m x 0 + b = b

In the other words, the y-intercept is b = 20

We are also given that T = 10 when h = 1, so

10 = m x 1 + 20

The slope of the line is m = 10 – 20 = -10 and the required linear function is

T = -10h + 20

 

b) The graph of the above equation is

User Loaded Image | CSIT Guide

The slope is m = -100c/km, and this represents the rate of change if temperature with respect to height

 

c) At a height of 1.5 km, the temperature is

T = -10 (2) + 20 = 00c

 

 

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