Lesson 18

1. What's the difference between the "partition function," Z, and the "grand partition function", ?

If you have a system which can have either 0 or 1 particle, and energies of either e/2 or -e/2, what would be the grand partition function ? Briefly explain why you have each term in your sum.

Enter your answer here:

2. The absolute activity is defined by l = exp(m/t).
Consider an ideal gas which has just its internal chemical potential, m_int. How would the absolute activity l change:

1. if the concentration of the gas doubled (and everything else remained constant)?
2. if the temperature doubled (and pressure stayed constant)?
3. if the pressure doubled (and temperature stayed constant)?

Enter your answer here:

3. The Grand Partition Function is the sum over all states of the system for all numbers of particles. This means there will be a term in the sum which is equal to 1 if:

Check the correct answer:
a) the number of particles starts at 0.
b) the number of particles starts at 0 and there is no external chemical potential.
c) the number of particles starts at 0 and the absolute activity is 0.
d) the number of particles starts at 0 and the energy for N=0 is assigned to be 0.

Below is a space for your thoughts, including general comments about today's assignment (what seemed impossible, what reading didn't make sense, what we should spend class time on, what was "cool", etc.):

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