Challenge Problems (Problem 121)

The temperature of the atmosphere is not always constant and can increase or decrease with height. In a neutral atmosphere, where there is not a significant amount of vertical mixing, the temperature decreases at a rate of approximately 6.5 K per km. The magnitude of the decrease in temperature as height increases is known as the lapse rate $(\text{Γ}).$ (The symbol is the upper case Greek letter gamma.) Assume that the surface pressure is $p_0=1.013\times {10}^5\text{Pa}$ where $\text{T}=293\text{K}$ and the lapse rate is $(-\Gamma =6.5\frac{\text{K}}{\text{km}})$. Estimate the pressure 3.0 km above the surface of Earth.