The canonical ensemble : Introductory video

Before watching the video read the questions below. As you watch the video try to answer them

Questions

    • Explain why function can be used to calculate the energy, number of atoms and volume of a microstate. What are the arguments of these functions?
    • What is the name of the function that is used to calculate the energy of a microstate.
    • Which extensive thermodynamic variables are constrained to have a particular value in the canonical ensemble.
    • Give an expression for the probability of being in a microstate in the canonical ensemble
    • Give an expression for the canonical partition function
    • Give an expression for $\frac{\textrm{d}S}{k_B}$ for the canonical ensemble that can be obtained using arguments based on statistical mechanics.
    • Explain why in the previous expression we can write terms such as $\left \langle \frac{ \partial H }{\partial N} \right\rangle$ and $\left \langle \frac{ \partial H }{\partial V} \right\rangle$
    • Give an expression for $\beta$ and explain how this result is derived.