2033 Consider a system of No non-interacting quantum mechanical oscilla- tors in equilibrium at temperature T. The energy levels of a single oscillator are Em = (m + 1/2)¬/V with m = 0, 1, 2... etc. %3D %3D (7 is a constant, the oscillators and volume V are one dimensional.)

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2033
Consider a system of No non-interacting quantum mechanical oscilla-
tors in equilibrium at temperature T. The energy levels of a single oscillator
are
Em
(m + 1/2)7/V with m 0, 1, 2... etc.
%3!
(y is a constant, the oscillators and volume V are one dimensional.)
(a) Find U and C, as functions of T.
(b) Sketch U(T) and C,(T).
(c) Determine the equation of state for the system.
(d) What is the fraction of particles in the m-th level?
(SUNY, Buffalo)
Transcribed Image Text:2033 Consider a system of No non-interacting quantum mechanical oscilla- tors in equilibrium at temperature T. The energy levels of a single oscillator are Em (m + 1/2)7/V with m 0, 1, 2... etc. %3! (y is a constant, the oscillators and volume V are one dimensional.) (a) Find U and C, as functions of T. (b) Sketch U(T) and C,(T). (c) Determine the equation of state for the system. (d) What is the fraction of particles in the m-th level? (SUNY, Buffalo)
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