Earth scape velocity is 11,200 m/s at sea level.Assume STP (Standar Temperature

Question

Earth scape velocity is 11,200 m/s at sea level.Assume STP (Standar Temperature and Pressure)

a)Calculate root mean square speed of Hydrogen gas at sea level. But Hydrogen floats to the top of the atmosphere, doesnt? The temperature on top of the atmosphere (Low Earth Orbit) is 4,530 oF and a pressure of 10-7 pascal. Escape velocityhereis 6,000 m/s.

b)Calculate the root mean square speed of Hydrogen gas at the top of the atmosphere.

c)Can Hydrogen escape Earth from sea level?

d)Can Hydrogen escape Eartth from Low Earth Orbit?

Explanation / Answer

a) at STP

T = 0 C = 0 + 273 = 273 K

molar mass of hydrogen, M = 2 gram/mole = 0.002 kg/mole

we know, vrms = sqrt(3*R*T/M)

= sqrt(3*8.314*273/0.002)

= 1845 m/s

a) at top of the atmosphere, Tc = (5/9)*(Tf - 32)

= (5/9)*(4530 - 32)

= 2499 c

T = 2499 + 273

= 2772 k

vrms = sqrt(3*R*T/M)

= sqrt(3*8.314*2772/0.002)

= 5880 m/s

c) No. because 1845 > > 11200 m/s

d) Yes, because, 5880 m/s is close to 6000 m/s

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