Atmospheric pressure

How and by how much hPa will the atmospheric pressure change when we take the cable car from Skalnate Pleso to Lomnický štít?
The altitudes of the cable car stations are 1754 m above sea level and 2634 m above sea level.

Correct answer:

Δ =  -80.32 hPa

Step-by-step explanation:

$$\begin{gathered} p_0=1013.25\cdot 100=101325\text{Pa} \\ g=9.81{\text{m/s}}^2 \\ \rho =1.2{\text{kg/m}}^3 \\ {h}_1=1754\text{m} \\ {h}_2=2634\text{m} \\ {p}_1=p_0\cdot e^{-\frac{\rho \cdot g\cdot h_1}{p_0}}=101325\cdot e^{-\frac{1.2\cdot 9.81\cdot 1754}{101325}}\doteq 82644.8398\text{Pa} \\ {p}_2=p_0\cdot e^{-\frac{\rho \cdot g\cdot h_2}{p_0}}=101325\cdot e^{-\frac{1.2\cdot 9.81\cdot 2634}{101325}}\doteq 74612.9029\text{Pa} \\ \Delta p=p_2-p_1=74612.9029-82644.8398\doteq -8031.9369\text{Pa} \\ \Delta =\Delta p/100=(-8031.9369)/100=-80.32\text{hPa} \end{gathered}$$

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