The temperature is 12 degress at an altitude of 2500m and -50 degrees at an altitude of 12500m. Determine m&b

Question

I do not know how to start of. The temperature of the atmosphere, T Degrees Celsius, is usually a linear function of the altitude, h metres. An equation of the function is T=mh+b, where m and b are constants to be determined

Answer 1

Treat your data like ordered pairs on a graph.

If 12=m2500+b
and -50=m12500+b
then you can solve those equations for m and b.

You can also try to find m without solving that system of equations, which will make it simpler to find b.

"m" stands for slope, which can also be defined as the change in "y" divided by the change in "x." In this case, it will be T divided h.

So, the slope is (-50-12)/(12500-2500)=-62/10000=.0062

Now you can say that 12=.0062*2500+b
and 12=15.5+ b
and -3.5=b

So, the function is T=.0062h-3.5

Follow all that?

Answer 2

Several problems with both the ? and the answers so far:

1) The standard atmosphere is a linear function up to only 11,000 meters, so using the input data to form a straight line will give nonsense results.

2) The previous answers fall victim to 1) by not noticing that b must equal the sea level standard temp, which they miss by a wide margin.

The correct input #s are -1.25 deg @ 2500 m and -56.5 deg @ 11000 m. Using these inputs, m is computed to be -.0065 and b is 16.5 deg, a number much closer to the sea level standard of 15 deg C

Answer 3

Use the following formula: T1-T2=m(H1-H2)
12-(-50)=m*(2500-12500)
Therefore, 62=M(-10000)
M=62/-10000
M=-.0062
To find B, solve: -50=12*25000*(-.0062)+B
B=-.0268