Question

The atmosphere of Mars is almost all carbon dioxide and the average surface pressure is 610 Pa (as compared with 101,000 Pa on Earth). A model for the temperature in the atmosphere is given by: T = To (e)^-Cz, where C m/s?. where C=1.1 E-5 /m. Assume ideal gas behavior. The gravitational acceleration is g = 3.71 m/s2. Determine: (a) analytic equation for the variation of pressure with altitude (b) the altitude [m] where the pressure is 10 Pa.

Answer 1

Answer:

   z = 3,737 10⁵ m

Explanation:

a) As they indicate that the atmosphere behaves like an ideal gas, we can use the equation

          P V = n R T

          P = (n r / V) T

We replace

         P = (n R / V) T₀ $e^{- C z}$

b) Let's apply this equation in the points

Lower

        .z = 0

         P₀ = 610 Pa

         P₀ = (nR / V) T₀

Higher.

         P = 10 Pa

          P = (n R / V) T₀ e^{- C z}

We replace

        P = P₀ e^{- C z}

        e^{- C z} = P / P₀

        C z = ln P₀ / P

        z = 1 / C ln P₀ / P

Let's calculate

        z = 1 / 1.1 10⁻⁵ ln (610/10)

        z = 3,737 10⁵ m