Answer:
The air temperature at the tropopause is - 79 °C
Explanation:
We know that a station near the equator has a surface temperature of 25°C
Vertical soundings reveal an environmental lapse rate of 6.5 °C per kilometer.
The tropopause is encountered at 16 km.
In order to find the air temperature at the tropopause we are going to deduce a linear function for the temperature at the tropopause.
This linear function will have the following structure :
[tex]f(x)=ax+b[/tex]
Where ''[tex]a[/tex]'' and ''[tex]b[/tex]'' are real numbers.
Let's write [tex]T(x)[/tex] to denote the temperature '' T '' in function of the distance
'' x '' ⇒
[tex]T(x)=ax+b[/tex]
We can reorder the function as :
[tex]T(x)=b+ax[/tex] (I)
Now, at the surface the value of ''[tex]x[/tex]'' is 0 km and the temperature is 25°C so in the function (I) we write :
[tex]T(0)=25=b+a(0)[/tex] ⇒ [tex]b=25[/tex] ⇒
[tex]T(x)=25+ax[/tex] (II)
In (II) the value of ''[tex]a[/tex]'' represents the change in temperature per kilometer.
Because the temperature decrease with the height this number will be negative and also a data from the question ⇒
[tex]T(x)=25-(6.5)x[/tex] (III)
In (III) we deduced the linear equation. The last step is to replace by [tex]x=16[/tex] in (III) ⇒
[tex]T(16)=25-(6.5)(16)=-79[/tex]
The air temperature at the tropopause is - 79 °C
