91Ó°ÊÓ

Evaluate the atmospheric pressure by the formula

$\mathit{P}\mathbf{=}{\mathit{P}}_{\mathbf{0}}{\mathit{e}}^{\frac{\mathbf{-}\mathbf{M}{\mathbf{a}}_{\mathbf{v}}\mathbf{y}}{\mathbf{R}\mathbf{T}}}$

where M=molar mass of carbon, a_v=acceleration due to the gravity on venus, y=height above the surface, R=gas constant and T= temperature

$$\begin{gathered} p=92atm{e}^{\frac{44×{10}^{-3}kg/mol×0.894×9.8m/s^2×1×{10}^{3}m}{8.314J/mol×\left(460+273.15\right)K}} \\ =86.362atm \end{gathered}$$

The atmospheric pressure above the surface of Venus by 1 km in earth-atmospheres is 86.362 atm.

Also, the atmospheric pressure above the surface of Venus by 1 km in Venus-atmospheres is$\frac{86.392atm}{92atm}=0.939atm$ .

The root mean square speed is given by where R is the molar gas constant,

$$\begin{gathered} u_{rms}=\sqrt{\frac{3RT}{m}} \\ =\sqrt{\frac{3×8.314J/mol.K×\left(460+273.15\right)K}{44×{10}^{-3}kg/mpl}} \\ =644.706m/s^2 \end{gathered}$$

So, the root-mean-square speed at the surface of Venus and at an altitude of 1 km is 644.706 m/s.