1. Find the average energy for an n-state system, in which a given state can have energy 0, e, 2e,..., ne 2. A harmonic oscillator, in which a given state can have energy 0, e, 2€,... (i.e., with no upper limit)
1. Find the average energy for an n-state system, in which a given state can have energy 0, e, 2e,..., ne 2. A harmonic oscillator, in which a given state can have energy 0, e, 2€,... (i.e., with no upper limit)
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Transcribed Image Text:: If a system is in contact with a reservoir and has a microstate r with energy
Er, then
P(microstater) =
where
k&T
In a two-state system, there are only two states, one with
energy 0 and the other with energy e > 0. The average energy of the system is
calculated below:
e-BE,
Σ; e-βE,
The probability of being in the lower state is given by the equation above, so
we have
1
1+ e-Be
Similarly, the probability of being in the upper state is
P(0)
=
P(e) =
e-Be
1+e-Be
The average energy <E> of the system is then
<E>=0* P(0) + € * P(e)
€
eße +1
1. Find the average energy <E> for an n-state system, in which a given
state can have energy 0, €, 2,..., ne
2. A harmonic oscillator, in which a given state can have energy 0, €, 2, ...
(i.e., with no upper limit)
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