14.7 Exercise 36

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 $\left(\Gamma\right) .$ (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 $\left(− \Gamma = 6.5 \frac{\text{K}}{\text{km}}\right)$. Estimate the pressure 3.0 km above the surface of Earth.