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quizsolnS10 - Quiz Solutions S10(Section 011 CHEM444 27th...

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Quiz Solutions: S10 (Section 011, CHEM444) 27th February 2010 1 Quiz 1 1.1 Problem 1 What is the ratio of the following values for a particle of Argon and Krypton at 298K? ν Ar ave ν Kr ave ν Ar ave ν Kr ave = r m Kr m Ar = r 83 . 798 39 . 948 = 1 . 45 ν Ar most probable ν Kr most probable ν Ar most probable ν Kr most probable = r m Kr m Ar ν Ar rms ν Kr rms ν Ar rms ν Kr rms = r m Kr m Ar 1
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1.2 Problem 2 What is the ratio of average kinetic energy of the two systems of Problem 1? < KE > Ar < KE > Kr = 1 We will show this the long way. < KE > Ar = Z 0 4 π m Ar 2 π k B T 3 / 2 1 2 m Ar ν 2 e ( - m Ar ν 2 / 2 k B T ) ν 2 = 1 2 m Ar ν 2 rms = 1 2 m Ar 3 k B T m Ar = 3 2 k B T < KE > Kr = Z 0 4 π m Kr 2 π k B T 3 / 2 1 2 m Kr ν 2 e ( - m Kr ν 2 / 2 k B T ) ν 2 = 1 2 m Kr ν 2 rms = 1 2 m Kr 3 k B T m Kr = 3 2 k B T Thus the ratio is 1 . For ideal gases, energy is a function of temperature. Note that the expression for the average kinetic energy we derived in this exercise is identically the result one would obtain from rigorous statistical mechanical treatment. The kinetic energy is related to the rms speed, not
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