The mission of the Cassini-Huygens spacecraft was explained as \"a four-year, cl

Question

The mission of the Cassini-Huygens spacecraft was explained as "a four-year, close-up study of the Saturnian system .. [including Saturn's largest moon] Titan." Cassini found several interesting facts concerning Titan's atmosphere: eg chttp: //www.windows, ucaredu/tour/link-lsaturn/moons/titan atmosphere overview.html&edu; = high >: The atmosphere consists mostly of nitrogen (for this problem, you may assume that the atmosphere is 100% nitrogen) The surface pressure is 60% greater than that of the earth's pressure at sea level Scientists suspect that methane falls as rain and snow on Titan, and that methane lakes may exist on the surface of Titan The surface temperatures are very cold (approx. -260 degree F) Given these conditions, determine the following: 1. The atmospheric pressure at the surface of Titan (psia) 2. The height above the surface of Titan (in ft) at which the pressure drops to 14.7 psia (typical atmospheric pressure at the earth's surface) 3. The depth in a methane lake at which the pressure is double that at the lake's surface (recall that on earth, the pressure in a lake doubles for every 30 feet of depth: is it the same on Titan?)

Explanation / Answer

1. Since the atmospheric pressure of Titan is 60% higher than that of earth. We know that the atmospheric pressure of earth is 14.7psi

60% of 14.7

60/100*14.7=8.82

Now 8.82+14.7=23.52 psi.

Therefore atmospheric pressure of Titan will be 23.52psia

2. For the atmosphere of the earth

atmospheric pressure at sea level=14.7psia

atmospheric pressure at an elevation of 10,000 feet=10.11 psia

Drop in pressure between the two=14.7-10.11=4.59psia

We know that

density of air=0.0765 lb/cft

density of nitrogen=0.0725 lb/cft

For every 10,000 feet drop in pressure of titan=4.59*0.0725/0.0765

=4.35 psia

For the pressure to drop to 14.7 psia the drop in pressure will be 23.52-14.7=8.82 psia

Elevation=8.82/4.35*10,000=20,276 ft

3. The pressure in lake doubles on earth doubles every 30 feet

We know that

Specific gravity of water=1

Specific gravity of methane at -164 degree celsius=0.466

Depth of methane lake at which pressure gets doubled=30/0.466

=64.37 ft

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