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Partition functions and probability

Imagine a particle that can be in only 3 states with energies 1 eV, 2 eV, and 3 eV. The particle is in equilibrium with a reservoir at 300 K.

a) Calculate the partition function for this particle.

b) Calculate the probability of the particle being in the 2 eV state.

c) How does the probability in part (b) change if the reservoir temperature is 3000 K?

Solution Preview

The partition function is:

Z = Sum_{r}Exp(-beta E_{r})

where the r label the states of the system and E_{r} is the energy of state r.

In this case the temperature is 300 K, and k T = 4.142*10^(-21) J = 2.585*10^(-2) ...

Solution Summary

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