Question

NASA is designing a mission to explore Titan, the largest moon of Saturn. Titan has numerous hydrocarbon lakes containing a mix of liquid methane and liquid ethane in unknown proportions. As part of the mission, a small submersible vehicle will explore Kraken Mare, the largest of these lakes. Assuming the maximum depth of Kraken Mare is less than 400 meters [m], how much total pressure in units of atmospheres [atm] must the submersible be designed to withstand? Assume the surface pressure on Titan is 147 kilopascals [kPa], the surface temperature is 94 kelvins [K], and the gravity is 1.35 meters per second squared [ m/s2]. The specific gravity of liquid methane is 0.415 and the specific gravity of liquid ethane is 0.546.

Answer 1

Answer:

Total pressure in atmosphere  IS 4.36 atm

Explanation:

Given Data:

Depth of lake is 400 mtr

surface tension is 147 kilopascals

surface temperature  94 kelvin

Gravity = 1.35 m/s^2

specific gravity of methane(liquid) = 0.415

specific gravity of ethane(liquid) = 0.546

density of methane can be obtained as

$\rho_{methane} = 0.415\times 1000 = 415 kg/m^3$

Density of ethane can be obtained as

$\rho_{ethane} = 0.546\times 1000 = 546 kg/m^3$

Total pressure in atmosphere can be obtained as

$P = surface\ tension + \rho_{max}gh$

 $= 147 +546\times 1.35\times 400\times 10^{-3}$

  = 441.84 kPa

$= 441.84\times 0.009869 atm\kPa$

 = 4.36 atm