ch19-p037

# ch19-p037 - 37. The rms speed of molecules in a gas is...

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() ( ) 26 3 3 2 0.16 9.8m s 1.74 10 m 32.0 10 kg mol 7.0 10 K. 38 .31Jmo lK T ×× == × (e) The temperature high in Earth's atmosphere is great enough for a significant number of hydrogen atoms in the tail of the Maxwellian distribution to escape. As a result the atmosphere is depleted of hydrogen. (f) On the other hand, very few oxygen atoms escape. So there should be much oxygen high in Earth’s upper atmosphere. 37. The rms speed of molecules in a gas is given by 3 rms vR T M = , where T is the temperature and M is the molar mass of the gas. See Eq. 19-34. The speed required for escape from Earth's gravitational pull is 2 e vg r = , where g is the acceleration due to gravity at Earth's surface and r e (= 6.37 × 10 6 m) is the radius of Earth. To derive this expression, take the zero of gravitational potential energy to be at infinity. Then, the gravitational potential energy of a particle with mass m at Earth's surface is 2 e e UG M m r m g r =− , where 2 e gG M r = was used. If v is the speed of the particle, then its total energy is 2 1 2 e E mgr mv + . If the particle is just able to travel far away, its kinetic energy must
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## This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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