Problem 5 (14 marks) The particles, of mass m, of an ideal single-atomic gas at temperature T are constrained to move in the x-y plane, making the gas effectively two-dimensional. Use a heuristic argument to determine the Maxwell speed distribution of this two dimensional gas. In other words, find the probability density p(v). p(v) determines the probability p(v)du that a particle has speed between v and v + dv or, equivalently, the fraction of particles in the gas that have speed between v and v + dv. Normalize the distribution and determine the most likely speed as well as the r.m.s speed. Do your findings agree with your intuition from the equipartition theorem? You may find these integrals useful: J dy e y = 1, J dy ye y = 1