InterviewSolution
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InterviewSolution
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Making use of the Maxwell distribution function, find `lt lt 1//v gt gt`, the mean value of the reciprocal of the velocity of molecules in an ideal at a temperature `T`, it the mass of eacd molecule is equal to `m`. Compare the value obtained with the reciprocal of the mean velocity. |
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Answer» `lt lt (1)/(v) gt gt = int_0^oo ((m)/(2 pi kT))^(3//2) e^((-mv^2)/(2 kT)) 4 pi v^2 dv (1)/(v)` =`((m)/(2 pi kT))^(3//2) 4 pi (1)/(2) (2 kT)/(m) int_0^oo e^-x dx` =`2((m)/(2 pi kT))^(1//2) = ((2 m)/(pi kT))^(1//2) = ((16)/(pi^2) (m pi)/(8 kT))^(1//2) = (4)/(pi lt v gt )`. |
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