Homework Assignments
1. Find the equation of state and the internal energy of an ideal gas at temperature T, confined to a volume V and made up of two kinds of atoms A and B. Do this problem in two ways, first using the canonical and then the grand-canonical ensemble. In the canonical ensemble, assume there are n1 atoms of type A and n2 atoms of type B. In the grand-canonical ensemble, assume that these are the expectation values of the corresponding quantities. Compare your results to one another and also to what you would expect from the equipartition theorem. 2. Find the equation of state and the internal energy of an ideal gas at temperature T, confined to a volume V and made up of molecules to be modeled by two equal mass atoms connected to one another with springs of stiffness constant k. Do this problem in two ways, first using the canonical and then the grand-canonical ensemble. In the canonical ensemble, assume there are n atoms in volume V. In the grand-canonical ensemble, assume that this is the expectation value of this quantity. Compare your result to what you would expect from the equipartition theorem.
Check the Stars system for your homework grade. In some cases, you may be able to re-submit your homework to the assistant with corrections and improve your grade.
Your homework grade average: HAV = 0.5 * ( HA + HG ) The arithmetic average: HA = ( ∑ GR + ∑ GE ) / NR The geometric average: HG = ( ∏ GR ) 1/NR GR = Required homework grades ( NR = number of such assignments ) GE = Extra credit homework grades