Show that when a system is in thermal and diffusive equilibrium with a reservoir, the average number of particles in the system is kT aZ N = z du where the partial derivative is taken at fixed temperature and volume. Show also that the mean square number of particles is (kT)? ô²z N2 = Use these results to show that the standard deviation of N is ON = kT(ƏN/Əµ), in analogy with Problem 6.18. Finally, apply this formula to an ideal gas, to obtain a simple expression for oN in terms of N. Discuss your result briefly.
Show that when a system is in thermal and diffusive equilibrium with a reservoir, the average number of particles in the system is kT aZ N = z du where the partial derivative is taken at fixed temperature and volume. Show also that the mean square number of particles is (kT)? ô²z N2 = Use these results to show that the standard deviation of N is ON = kT(ƏN/Əµ), in analogy with Problem 6.18. Finally, apply this formula to an ideal gas, to obtain a simple expression for oN in terms of N. Discuss your result briefly.
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Transcribed Image Text:Show that when a system is in thermal and diffusive equilibrium
with a reservoir, the average number of particles in the system is
kT aZ
N =
z du
where the partial derivative is taken at fixed temperature and volume. Show also
that the mean square number of particles is
(kT)? ô²z
N2 =
Use these results to show that the standard deviation of N is
ON =
kT(ƏN/Əµ),
in analogy with Problem 6.18. Finally, apply this formula to an ideal gas, to obtain
a simple expression for oN in terms of N. Discuss your result briefly.
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