Lattice Gasses : Introductory video
Before watching the video read the questions below. As you watch the video try to answer them
Questions
- What two factors is it important to consider when calculating the partition function for a model system?
- What Hamiltonian is stuided in this video? What do all the terms in the Hamiltonian describe? What does the sum run over?
- How many states can each of the spins be in?
- Why is it significant that each term in the summation in the Hamiltonian depends on the value of only one spin variable?
- Suppose each spin could be in one of three states rather than one of two states. How many different microstates would there be for a system containing $N$ such spins?
- Explain why (using the arguments in the video) the partition function for the lattice spins is $Z=2^N \cosh(\beta \mu H)$
- How is the average energy of the system calculated from the partition function? What is the average energy for the system of spins under study in this exercise?
- What happens to the the average energy of the system in the low and high-temperature limits? What does this imply about the behavior of the psins?
- What two factors is it important to consider when calculating the partition function for a model system?
- What Hamiltonian is stuided in this video? What do all the terms in the Hamiltonian describe? What does the sum run over?
- How many states can each of the spins be in?
- Why is it significant that each term in the summation in the Hamiltonian depends on the value of only one spin variable?
- Suppose each spin could be in one of three states rather than one of two states. How many different microstates would there be for a system containing $N$ such spins?
- Explain why (using the arguments in the video) the partition function for the lattice spins is $Z=2^N \cosh(\beta \mu H)$
- How is the average energy of the system calculated from the partition function? What is the average energy for the system of spins under study in this exercise?
- What happens to the the average energy of the system in the low and high-temperature limits? What does this imply about the behavior of the psins?