A canister of 1.00 m o l of nitrogen gas (28.0 g / m o l ) at 30.0 %u2218 C is l

Question

A canister of 1.00mol of nitrogen gas (28.0g/mol) at 30.0%u2218C is left on Jupiter's satellite after completion of a future space mission. Europa has no appreciable atmosphere, and the acceleration due to gravity at its surface is 1.30 m/s2. After some time, the canister springs a small leak, allowing molecules to escape through a small hole.

What is the maximum height (in km) above Europa's surface that a N2 molecule having speed equal to the rms speed will reach if it is shot straight up out of the hole in the canister? Ignore the variation ing with altitude,

a) h = ?

Explanation / Answer

Vrms = sqrt(3RT/M)

M=molar mass = 28 g/mol = 0.028kg/mol

T = 273.15+30 = 303.15 K

so,

Vrms = sqrt(3*8.314*303.15/0.028) = 519.655 m/s

as,

u =Vrms

and at max height v = 0

from

v^2 = u^2 +2as

we get

s = u^2/(-2a)

a = -1.30

so,

s = 519.655^2/(-2*-1.30) = 103862.045 m

so,

max height reached = 103862.045 m = 103.862 km

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