Question

The mesosphere is the layer of Earth's atmosphere between 50 kilometers and 85 kilometers above Earth's surface. At a distance of 50 kilometers from Earth's surface, the temperature in the mesosphere is $-5^o$ Celsius, and at a distance of 80 kilometers from Earth's surface, the temperature in the mesosphere is $-{80}^o$ Celsius. For every additional 10 kilometers from Earth's surface, the temperature in the mesosphere decreases by $k^o$ Celsius, where k is a constant. What is the value of k ?

Answer 1

At $50$ kilometer from earth's surface, the temperature is $-5^{o}C$

At $80$ kilometer from earth's surface, the temperature is $-{80}^{o}C$

Also, for every 10 kilometer, the temperature decreases by k degree C.

$\therefore -5-k\left(\frac{80-50}{10}\right)=-80$

$\Rightarrow -5+80=3\times k$

$\therefore k=25$