Question

Saturn's moon Titan has a mass of  1.3452 x 10²³ kg , a diameter of 5,150 km, and an atmosphere made mostly of N_{2  at a constant temperature of  -179 degrees Celsius .  Assume that the pressure at the surface is 50% more than on Earth.}

1. What is your best estimate of Titan's atmosphere's R constant?
2. Use Excel to make a table that shows up to a geometric altitude of 10 km (in steps of 1000 m) pressure, and density in SI consistent units.  

Answer 1

Step 1

We have univral gas constant. R = 8.314J/molK

For N₂ , molar mass= 28 g/mol

S​​​​​o titans atmospheric gas constant R`=universal GS constant/ molar mass

= 8.314/28 J/gK = 0.296 J/gK

Step2

We next find gravity on titans surface,

​​​​g =GM/R²

= (6.67*10^-11*1.3452*10^23)/ (2575*10^3)²

= 1.353m/s².

Then we calculate scale heght for pressure

1/H = g/RT = 1.353/(0.296*94) m^-1 = 0.0486 m^-1

So P = P₀e^-z/H

As P₀ = 1atm

p =1.5* exp(-z/0.0486) atm

Where 'z' is the height from 0 km to 10km .

And also density = P/R'T = P/ 0.296*94

Here P_{0 = 1.03*10^5 pa}

_{so density = 3.63 exp( -z/64.47) kg/m³}

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