The partition function of a system of particles is a statistical measure that describes the distribution of particles over different energy states.
It is defined as:
Z = Σexp(-E_i/kT)
where Z is the partition function, E_i is the energy of the i-th particle, k is the Boltzmann constant, and T is the temperature of the system. The sum is taken over all possible energy states of the particles.
In the case of a system of volume v and temperature t consisting of n independent, distinguishable particles, each of which can be in one of two states with energy equal to 0 or e, the partition function can be expressed as:
Z = exp(-0/kT) + exp(-e/kT)
This is because there are two possible energy states for each particle (0 or e), and the partition function is a sum over all possible energy states of the particles.
Substituting the values of k, T, and e into the partition function equation, we can compute the value of Z:
Z = exp(-0/kT) + exp(-e/kT)
= exp(0) + exp(-e/kT)
= 1 + exp(-e/kT)
Thus, the partition function of the system is given by the equation:
Z = 1 + exp(-e/kT)
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