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Unformatted text preview: Using n = N/N A and R = N A k B leads to, m atom <v 2 >/3V = k B T or E int one atom = m atom <v 2 > = 3/2 k B T. If there are N atoms or n = N/N A moles, this becomes, E int = 3/2 nRT (for a monatomic ideal gas = m.i.g.) In summary, (i) the internal energy of an ideal gas depends only on its absolute temperature; (ii) temperature is a measure of the random kinetic energy of atoms; (iii) this equation is remarkable since it provides a connection between the macroscopic world (n, T) and the microscopic world (E int of a gas of atoms), (iv) and finally this results conforms to equipartition theorem where E int = no. degrees of freedom x k B T. Since the internal energy of a m.i.g. is entirely kinetic we have E int = m sample <v 2 > = 3/2 n R T, which gives the root mean square speed of an atom of the gas v RMS = [ 3RT/M] 1/2 . Caution: Keep straight n, N, N A , m atom , m sample , and M. These are six distinct quantities. EXAMPLES [in class]...
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 Spring '08
 Chen
 Physics, Force

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